ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 We also observe a peak at ~ zero lag in the AN-rav/optical cross-correlation function., We also observe a peak at $\sim$ zero lag in the X-ray/optical cross-correlation function.3 Its presence iuMies that the optical aud N-rav variatious are positevelv correlated but he statistical siguificauce of the peak is low., Its presence implies that the optical and X-ray variations are positevely correlated but the statistical significance of the peak is low.4 We now cliscuss our results in terms of models for ACN which involve X-ray reprocessing mechanisis for the xoduction of the UV/optical emission iu these objects., We now discuss our results in terms of models for AGN which involve X-ray reprocessing mechanisms for the production of the UV/optical emission in these objects.5 Due to the low statistical significance of the X-ray/optical cross-correlation peas and of the time delays within he optical bands. the scenarios that we discuss below based on these results should be considered as suggestive physical interpretations.," Due to the low statistical significance of the X-ray/optical cross-correlation peak and of the time delays within the optical bands, the scenarios that we discuss below based on these results should be considered as suggestive physical interpretations."6 Deuser optical light curves are needed in order to confri the correlation between the N-rayv and optical variations and the existence of time delavs within the optical baud in this source. allowiug a nore quantitatively ¢iscussiou of the predictions of respective plysical models.," Denser optical light curves are needed in order to confirm the correlation between the X-ray and optical variations and the existence of time delays within the optical band in this source, allowing us a more quantitatively discussion of the predictions of the respective physical models."7" It is generally assumed that the N-ravs in ACN arise from within a few immerimost radii (3R,. where Ry, is the Sclovarzschild radius) of a supermassive black hole."," It is generally assumed that the X-rays in AGN arise from within a few innermost radii $\sim 3R_s$, where $R_{s}$ is the Schwarzschild radius) of a supermassive black hole."8" There is lot of evidence from X-ray euerey spectral observations. mainly fi6 GL keV iron liue aud the so called ""Compton bunp (Nandra Pots 1991). that the N-rav source in ACN ilhuninaes a relatively dense and cool material (i.c. the accretioi disc)."," There is lot of evidence from X-ray energy spectral observations, mainly the 6.4 keV iron line and the so called “Compton bump"" (Nandra Pounds 1994), that the X-ray source in AGN illuminates a relatively dense and cool material (i.e. the accretion disc)."9 If that is the case. the heated dise is expected to radiae iu the ultravioletfoptical as well.," If that is the case, the heated disc is expected to radiate in the ultraviolet/optical as well."10 So X-ravs could be responsible for some or all of the optical radiation via reprocessing (Culbert Rees 1985)., So X-rays could be responsible for some or all of the optical radiation via reprocessing (Guilbert Rees 1988).11 Iu fact. some Componisation models which provide a good agreement with he observed X-ray energy spectra of ACN. assune a specific geometry which involves a slaly of jieutral material subtending a solid angle of 27 st to the N-vay source located above the slab (eg Taarcdt Maraschi 1991).," In fact, some Comptonisation models which provide a good agreement with the observed X-ray energy spectra of AGN, assume a specific geometry which involves a slab of neutral material subtending a solid angle of $2\pi$ sr to the X-ray source located above the slab (eg Haardt Maraschi 1991)."12 The N-rav huuinositv of is Lostuk~2s.104 ere + (CLeighly 1999a. Vaughan et al.," The X-ray luminosity of is $L_{0.5-10~{\rm keV}} \sim 2 \times1310^{44}$ erg $^{-1}$ (Leighly 1999a, Vaughan et al."14 1999)., 1999).15 The suu of the mean D.V.R aud Z luuinosity durius our mnonitoriug campaign is ~0.9«10t ere 1," The sum of the mean $B,V,R$ and $I$ luminosity during our monitoring campaign is $\sim160.9\times 10^{44}$ erg $^{-1}$."17 Under t10 assuniptio1 that half of the t1ο N-rav flux is heating the dise. we expect the N-ravs to affec the disc output senificautlv i1 Consequently. we should observe optical variations which follow hose iun the X-rav band. perhaps smioothed out (below a ceran tine scale) due to geometric. liebt travel time and variability amplitude of is ~20 times that in the optical.," Under the assumption that half of the the X-ray flux is heating the disc, we expect the X-rays to affect the disc output significantly in Consequently, we should observe optical variations which follow those in the X-ray band, perhaps smoothed out (below a certain time scale) due to geometric, light travel time and variability amplitude of is $\sim 20$ times that in the optical."18 This result aloue strongly sugeests that most of f16 optical chussion in isnot reprocessed X-ray ciuission bv optically thick material., This result alone strongly suggests that most of the optical emission in is reprocessed X-ray emission by optically thick material.19 Either ouly a simall part of the disc is seem bx the N-rayv source (1.0. the N-rav source is2of located above the disk but iu its inermost part and las a small height so the solid angle subteuded by the dise is small) or the AX-ravs are not isotropically cuutted (1.0. most of the N-rav flux is emitted away from the disc)., Either only a small part of the disc is seen by the X-ray source (i.e. the X-ray source is located above the disk but in its innermost part and has a small height so the solid angle subtended by the disc is small) or the X-rays are not isotropically emitted (i.e. most of the X-ray flux is emitted away from the disc).20 Furthermore. our optical campaign revealed sinall wuplitude. but statistically significant optical variations.," Furthermore, our optical campaign revealed small amplitude, but statistically significant optical variations."21 These are observed at all optical bands and are well correlated (with a asin time lag of ~2 davs) within the different bands., These are observed at all optical bands and are well correlated (with a maximum time lag of $\sim 2$ days) within the different bands.22 What could be their origin?, What could be their origin?23 Omne possibility is that some part of the X-ray emission is. after all. heating the disk. produce a reprocessed. variable optical component.," One possibility is that some part of the X-ray emission is, after all, heating the disk, producing a reprocessed, variable optical component."24 In this case. we expect to observe a time delav between the reprocessed. optical aud X-ray chussion of the order of 7~ Rc. where Ris the distance between the X-ray source and the re-processing region.," In this case, we expect to observe a time delay between the reprocessed optical and X-ray emission of the order of $\tau \sim R/c$ , where $R$ is the distance between the X-ray source and the re-processing region."25 We do observe a time lag of 7~1 dav between N-rav iid optical variations., We do observe a time lag of $\tau\sim 1$ day between X-ray and optical variations.26 Ef this is real (which implics that, If this is real (which implies that27We reduced the data using the 7.0.0 version of the Science Xnalvsis System (SAS): the standard analysis methods using this software are described in e.g. ?..,We reduced the data using the 7.0.0 version of the Science Analysis System (SAS); the standard analysis methods using this software are described in e.g. \citet{Watson01}.28 We subtracted the instrumental background from the EPIC spectra using ¢losed-Lilter observations which were normalized to match our observation using the count rates in the hard. energy band (1012 keV for MOS. 1914 keV for pn) outside of the field of view (OobloV).," We subtracted the instrumental background from the EPIC spectra using closed-filter observations which were normalized to match our observation using the count rates in the hard energy band $10-12$ keV for MOS, $12-14$ keV for pn) outside of the field of view (OoFoV)."29 Out-ol-time events were subtracted from the EPIC/pn data using the standard SAS prescription for the extended. full frame mode., Out-of-time events were subtracted from the EPIC/pn data using the standard SAS prescription for the extended full frame mode.30" ""Phe cosmic X-ray background (CNB) obtained from spectra extracted from an annulus between aanel ((outside the clusters rsou) is modeled with three components: two thermal components to account for the ocal hot. bubble (CLIID) emission (AZ,=0.08) keV) and for the Calactic halo. (6011) emission (AZ~02 keV). as οποίος by 2.. and a power-law to account or the integrated emission. of unresolved point sources and for possible contamination from the residual soft woton particle background."," The cosmic X-ray background (CXB) obtained from spectra extracted from an annulus between and (outside the cluster's $r_{500}$ ) is modeled with three components: two thermal components to account for the local hot bubble (LHB) emission $kT_1 = 0.08$ keV) and for the Galactic halo (GH) emission $kT_2 \sim 0.2$ keV), as described by \citet{kuntz2000}, and a power-law to account for the integrated emission of unresolved point sources and for possible contamination from the residual soft proton particle background."31 Since dillerent. detectors. can »e alfected. dilferentlv. by soft. protons. we leave the power-aw indices ancl normalizations free between EPIC/AIOSL. ALOS2 ancl pn.," Since different detectors can be affected differently by soft protons, we leave the power-law indices and normalizations free between EPIC/MOS1, MOS2 and pn."32 The temperature of the LILB was frozen to 1.08 ke while the temperature of the GL and the spectrum normalizationsV. of the thermal components were free in the it. but. constrained. to be the same for all three LEPLC detectors.," The temperature of the LHB was frozen to 0.08 keV, while the temperature of the GH and the spectrum normalizations of the thermal components were free in the fit, but constrained to be the same for all three EPIC detectors."33 The spectra were fit in the O47., The spectra were fit in the 0.4–7.34 keV. energy ud., keV energy band.35 The RGS spectra were extracted. following the method described. by 2..., The RGS spectra were extracted following the method described by \citet{tamura2001b}.36 We modeled. the background. using the standard background model available in SAS (rgsbkgmodel..7).," We modeled the background using the standard background model available in SAS \citep[{\texttt{rgsbkgmodel}},."37 Phe cluster spectra were extracted [rom a region which is wwide in the cross-clispersion direction of the instrument., The cluster spectra were extracted from a region which is wide in the cross-dispersion direction of the instrument.38 The line emission. observed. with the RCS [rom extended sources js broadened by the spatial extent of the source along the clispersion direction., The line emission observed with the RGS from extended sources is broadened by the spatial extent of the source along the dispersion direction.39 In order to account for the line broadening in the spectral modeling. we convolve the line spread. Function (Is) model with the surface brightness profile of the source along the dispersion direction derived in the OS1.4 keV. band.," In order to account for the line broadening in the spectral modeling, we convolve the line spread function (lsf) model with the surface brightness profile of the source along the dispersion direction derived in the 0.8–1.4 keV band."40 We fit the Ist order spectra in the wavelength band of S25 aand the second order spectra in a narrower band of S16 AX., We fit the 1st order spectra in the wavelength band of 8–25 and the second order spectra in a narrower band of 8--16 .41 The Ist an 2nd order spectra. obtained by. the two RGS detectors were Π simultaneously with the relative instrument normalizations left as free parameters., The 1st and 2nd order spectra obtained by the two RGS detectors were fit simultaneously with the relative instrument normalizations left as free parameters.42" Freezing the Galactic absorbing column density. (ng) to 6107""em? as determined. from. 7? from 21 cm observations. gives very poor fits to the cluster. EPIC spectra."," Freezing the Galactic absorbing column density $n_{\rm H}$ ) to $6\times10^{20}\:\rm{cm}^{-2}$, as determined from \citet{dickey1990} from 21 cm observations, gives very poor fits to the cluster EPIC spectra."43" Therefore. we froze the mg to 8.7107""em the best-fit value. determined. by fitting EPIC spectra of the central 5’ in combination with ROSAT All-Skyv Survey (RASS) spectra to better constrain the emission in the soft X-ray band."," Therefore, we froze the $n_{\rm H}$ to $8.7\times10^{20}\:\rm{cm}^{-2}$, the best-fit value determined by fitting EPIC spectra of the central $5^\prime$ in combination with ROSAT All-Sky Survey (RASS) spectra to better constrain the emission in the soft X-ray band."44 Vhis value agrees within the confidence interval with the ry value computed from the 100 jm IH data. using the 7. LR-ny correlation function (more details will be provided by Mois et al.," This value agrees within the confidence interval with the $n_{\rm H}$ value computed from the 100 $\mu$ m IR data, using the \citet{Boulanger96} $n_{\rm H}$ correlation function (more details will be provided by Moiş et al.,"45 in prep), in prep).46 ‘To determine the amount of ICM. eas cooling out of the X-ray emitting temperature range. we extracted the LEPLC spectrum from a circle of radius 140 kpe (0.679) centred on he cluster centre.," To determine the amount of ICM gas cooling out of the X-ray emitting temperature range, we extracted the EPIC spectrum from a circle of radius 140 kpc ) centred on the cluster centre."47 This is the cooling radius obtained by ? or a Hubble constant 4o of TO kms | |., This is the cooling radius obtained by \cite{Boehringer1504} for a Hubble constant $H_0$ of 70 km $^{-1}$ $^{-1}$.48 The spectrum is fitted. with a Galactically absorbed single temperature collisionally ionized optically thinreeked xdasma model plus a classical cooling How model (with he lower cutoll temperature fixed to 0.1. keV)., The spectrum is fitted with a Galactically absorbed single temperature collisionally ionized optically thin plasma model plus a classical cooling flow model (with the lower cutoff temperature fixed to 0.1 keV).49 To ensure a correct propagation of errors due to uncertainties. in xkeround. determination. the EPIC source. spectra are it in parallel with the CAB spectra. obtained. [rom an outer annulus.," To ensure a correct propagation of errors due to uncertainties in background determination, the EPIC source spectra are fit in parallel with the CXB spectra obtained from an outer annulus."50 “Phe normalizations of the cluster spectral components were set to zero for the CAB data sets. while he normalizations of the background mocels were fixed for he source analysis to à ratio corresponding to the relative sizes of the extraction regions for the source and CXD only.," The normalizations of the cluster spectral components were set to zero for the CXB data sets, while the normalizations of the background models were fixed for the source analysis to a ratio corresponding to the relative sizes of the extraction regions for the source and CXB only."51 The metal abundances were coupled between the single emperature ancl cooling How models both for fitting the EPIC and the RGS data., The metal abundances were coupled between the single temperature and cooling flow models both for fitting the EPIC and the RGS data.52 The O/ke. Ne/EFe and Ale/be ratios were fixed in the EPIC fit based. on the best-fit values obtained from the HOS spectra. since the energy resolution and effective area calibration of EPIC around the energy of the O. Mg and Ne lines are too poor to allow a reliable determination of their abundances with EPIC alone. especially for such a hot cluster.," The O/Fe, Ne/Fe and Mg/Fe ratios were fixed in the EPIC fit based on the best-fit values obtained from the RGS spectra, since the energy resolution and effective area calibration of EPIC around the energy of the O, Mg and Ne lines are too poor to allow a reliable determination of their abundances with EPIC alone, especially for such a hot cluster."53 Phe Si and ο abundances of he hot plasma can only be measured with EPIC because the emission lines of these elements lie outside the GS energy xx., The Si and S abundances of the hot plasma can only be measured with EPIC because the emission lines of these elements lie outside the RGS energy band.54 “Phe fit results are summarized in Table 2.., The fit results are summarized in Table \ref{tab:rgs}. .55 Errors are quoted at the Le level., Errors are quoted at the $1\sigma$ level.56 Abuncance ratios are given in woto-solar units (?).., Abundance ratios are given in proto-solar units \citep{Lodders}.57 The high luminosity and the highly peakecl surface rightness distribution of the cooling core in RAC.1504.1-Y48 allow us to obtain relatively sensitive NMM-Neywton tGS spectra of this cluster despite its large distance., The high luminosity and the highly peaked surface brightness distribution of the cooling core in RXCJ1504.1-0248 allow us to obtain relatively sensitive XMM-Newton RGS spectra of this cluster despite its large distance.58 We show in Fig., We show in Fig.59 2. the spectrum obtained by combining data rom the two RGS detectors., \ref{fig:rgs} the spectrum obtained by combining data from the two RGS detectors.60 This is one of the most distant galaxy cluster spectra obtained. with RCs., This is one of the most distant galaxy cluster spectra obtained with RGS.61 The cause for he ciscrepaney between the temperatures measured. with EPLC and ROS is the different spectral extraction region (the RGS extraction region is ellectively -—long in the dispersion direction. ancl 2'--wide in thecross-dispersion, The cause for the discrepancy between the temperatures measured with EPIC and RGS is the different spectral extraction region (the RGS extraction region is effectively -long in the dispersion direction and -wide in thecross-dispersion62"in the My. (boy), diagram using a constant afe]=10.30 dex and interpolated) for the metal abuncances of ΑΗ=0.30.O40.0.52.0.61.0.70.(0.83.1.01 dex.","in the $M_{\rm V}$ , $(b-y)_{o}$ diagram using a constant $[\alpha/Fe]= +0.30$ dex and interpolated for the metal abundances of $[M/H]=-0.30, -0.40, -0.52, -0.61, -0.70, -0.83, -1.01$ dex."63 At sub-solar M/L] we assumed a/fe]=|0.30 dex or thick-disk stars with Al/L/]=O.S dex. taking into consideration Fig.," At sub-solar [M/H] we assumed $[\alpha/Fe]= +0.30$ dex for thick-disk stars with $[M/H]\la -0.8$ dex, taking into consideration Fig."64 3 of Wheeler. Sneden Truran (1989).," 3 of Wheeler, Sneden Truran (1989)."65 In order to estimate the errors for the age interpolations. he uncertainties (oy. and a 4) in V. and (b.y) have »en. collected. from the web site of the General Catalogue of Photometric Data of Hauck Alermilliocl (1998). and rom the Lipparcos and. Z'ycho catalogues 11991). he uncertainties (02/x) in the parallaxes (x) of our sample of stars given in Table 2.," In order to estimate the errors for the age interpolations, the uncertainties $\sigma_{\rm V}$, and $\sigma _{b-y}$ ) in $V$, and $(b-y)$ have been collected from the web site of the General Catalogue of Photometric Data of Hauck Mermilliod (1998), and from the $Hipparcos$ and $Tycho$ catalogues 1997), the uncertainties $\sigma_{\pi}/\pi$ ) in the parallaxes $\pi$ ) of our sample of stars given in Table 2."66" The derived error. equation or the Pogson relation given in Section 4.2. a,OV 2X7(o./x). allows us to estimate ay. from the uncertainties in V and w of individual stars in our sample."," The derived error equation for the Pogson relation given in Section 4.2, $\sigma _{M_{\rm V}}=\sigma_{\rm V} + 2.17(\sigma_{\pi}/\pi)$ , allows us to estimate $\sigma _{M_{\rm V}}$ from the uncertainties in $V$ and $\pi$ of individual stars in our sample."67 The resulting average uncertainties in A/y and (b.y) are 0.081 and 0.003 mag. respectively.," The resulting average uncertainties in $M_{\rm V}$ and $(b-y)$ are 0.081 and 0.003 mag, respectively."68 For stars bing along the turn-olfs of the isochrones. these average uncertainties in Aly and (b.y) result in age errors of ~ 1 Gyr when applied to the cilference between two isochrones in the Ady. (by). ciagram.," For stars lying along the turn-offs of the isochrones, these average uncertainties in $M_{\rm V}$ and $(b-y)$ result in age errors of $\sim$ 1 Gyr when applied to the difference between two isochrones in the $M_{\rm V}$, $(b-y)_{o}$ diagram."69 For sub-giants above the turn-olls. the errors are somewhat larger. LO01.5 Car.," For sub-giants above the turn-offs, the errors are somewhat larger, $1.0-1.5$ Gyr."70 Below the turn-olls the age errors can grow indefinitely due to the convergence of the isochrones., Below the turn-offs the age errors can grow indefinitely due to the convergence of the isochrones.71 We have measured ages to an error limit of about #2.5r Cvr., We have measured ages to an error limit of about $\pm 2.5$ Gyr.72 Error bars corresponding to an uncertainties of ] Gyr in age and 0.12.0.14 dex in. Fe/H]. (Schuster Nissen 1989 and Section 4.3) are indicated in Fig.," Error bars corresponding to an uncertainties of 1 Gyr in age and $0.12-0.14$ dex in $[Fe/H]$, (Schuster Nissen 1989 and Section 4.3) are indicated in Fig."73 9a., 9a.74 In Fig., In Fig.75 9a the metallicity is plotted as a function of age with cillerent svmbols for the definitive thin disk: (circles. No 33). probable thin disk (cross signs. 33<VY 31) ancl probable thick disk (plus signs. 21X< 6).," 9a the metallicity is plotted as a function of age with different symbols for the definitive thin disk (circles, $X \leq-33$ ), probable thin disk (cross signs, $-33 < X < -21$ ) and probable thick disk (plus signs, $-21 \leq X \leq-6$ )."76 It can be seen from Fig., It can be seen from Fig.77 9a that [ew stars have ages less than 3 Gyr: this is to be expected since the stars of this sample by Nidever et al. (, 9a that few stars have ages less than 3 Gyr; this is to be expected since the stars of this sample by Nidever et al. (782002) contain mostly late F-. Ge. and ]x-tvpe stars.,"2002) contain mostly late F-, G-, and K-type stars."79 This. derived age-metallicity relation agrees qualitatively with that of Edvardsson ct al. (, This derived age-metallicity relation agrees qualitatively with that of Edvardsson et al. (801993).,1993).81 A slight trend that metallicity decreases with increasing age is seen in Fig., A slight trend that metallicity decreases with increasing age is seen in Fig.82 9b: the slope of a least squares Π to the <MH] versus age is —0.01+0.005 dex L, 9b; the slope of a least squares fit to the $<[M/H]>$ versus age is $-0.01 \pm 0.005$ dex $^{-1}$.83 Even though there is this overall trend. of decreasing mean metallicity with increasing age. both a [larger scatter in MM] at a given age and the presence of old. metal-rich stars makeit dillieult to decide whether or not an age-metallicity relation really exists for the thin disk.," Even though there is this overall trend of decreasing mean metallicity with increasing age, both a larger scatter in [M/H] at a given age and the presence of old, metal-rich stars makeit difficult to decide whether or not an age-metallicity relation really exists for the thin disk."84 So. it is cüllieult to draw. any clear conclusion from Fig.," So, it is difficult to draw any clear conclusion from Fig."85 9a., 9a.86 The age-metallicity relations derived from the larger, The age-metallicity relations derived from the larger87 3CHa8 is a beautiful example of a filled-ceuter (or pleriouic) supernova ronunant (SNB). probably associated with the historical supernova event in List A.D. (27)).," 3C58 is a beautiful example of a filled-center (or plerionic) supernova remnant (SNR), probably associated with the historical supernova event in 1181 A.D. \cite{ste71}) )."88 This object has always received. much attention because. on the one hand. it shows some characteristics simular to the Crab SNR. while. on the other hand. it ποσα» very different to the Crab itself.," This object has always received much attention because, on the one hand, it shows some characteristics similar to the Crab SNR, while, on the other hand, it seems very different to the Crab itself."89" For instance. 3€758 has à compact (10« 6) elliptical morphology with a verv bright core (27)) and linear size similar to the Cral: 77. have reported a wisp-like elongated structure at 2.6"" from the core. which has beeu observed also in the Crab and which is probably associated with the pulsar wind termination shock."," For instance, 3C58 has a compact $10^\prime\times 6^\prime$ ) elliptical morphology with a very bright core \cite{ra88}) ) and linear size similar to the Crab; \cite*{fm93} have reported a wisp-like elongated structure at $2.6\arcsec$ from the core, which has been observed also in the Crab and which is probably associated with the pulsar wind termination shock."90 Towever. unlike the Crab. there is no clear evidence of a pulsating point source located iu the ceuter. as would ο expected. since the morphology strongly sugeest that he nebula is powered by a spinning neutrou star.," However, unlike the Crab, there is no clear evidence of a pulsating point source located in the center, as would be expected, since the morphology strongly suggest that the nebula is powered by a spinning neutron star."91 Despite considerable effort. pulsations have not been detected so ‘ar in ether radio (see e.g. ?7)). nor iu N-ravs (?7.. II95 jereafter).," Despite considerable effort, pulsations have not been detected so far in either radio (see e.g. \cite{llc98}) ), nor in X-rays \cite{hbw95}, H95 hereafter)."92 Moreover. the N-rav to radio flux ratio (fy/ f.) of 3C58 is LOO times lower than that of the Crab (II95). its spectral break occurs at 50 Gz (300 times less than he break of the Crab. ??)}) aud its radio Wuuiuositv is increasing instead of decreasiug as expected (27)).," Moreover, the X-ray to radio flux ratio $f_X/f_r$ ) of 3C58 is 100 times lower than that of the Crab (H95), its spectral break occurs at 50 GHz (300 times less than the break of the Crab, \cite{gs92}) ) and its radio luminosity is increasing instead of decreasing as expected \cite{gre87}) )."93" These renmniarkable differences are also seen in other plerious. aud TY have proposed the iutroductiou of a new sub-class of plerious. the ""uou. Crab-like plerious'. of which 3058 can be considered the prototype."," These remarkable differences are also seen in other plerions, and \cite*{wsp97} have proposed the introduction of a new sub-class of plerions, the “non Crab-like plerions"", of which 3C58 can be considered the prototype."94 For these objects. à uou-standard evolution of the pulsar can be invoked. but the details are not vet clear.," For these objects, a non-standard evolution of the pulsar can be invoked, but the details are not yet clear."95 It is therefore very duportaut to investigate the physica properties which render 3€58 so peculiar. iun order to put this object and its sub-class in the right perspective.," It is therefore very important to investigate the physical properties which render 3C58 so peculiar, in order to put this object and its sub-class in the right perspective."96 Iu particular. the detection or non-detection of the ceutral source is obviously a kev poiut.," In particular, the detection or non-detection of the central source is obviously a key point."97 ??7. reported the presence of a compact N-rav source in 3€758 from thei Einsteiu IIRI observation. abou in extent. ane coutributing to of the detected N-rav flux.," \cite*{bhs82} reported the presence of a compact X-ray source in 3C58 from their Einstein HRI observation, about in extent, and contributing to of the detected X-ray flux."98 Later. TT vevisited the N-ray ciission of 3C5s using ROSAT IIRI data. coufirmine the compact source and favored a aodel in terius of hot polar caps to explain the cussion.," Later, \cite*{hbw95}99 revisited the X-ray emission of 3C58 using ROSAT HRI data, confirming the compact source and favored a model in terms of hot polar caps to explain the emission."100 Towever. it has not been possible so far to take an X-ray spectrum of the source to study it. aud to uclerstand ifit is really a point source or an enliaucemen f the pulsar nebula.," However, it has not been possible so far to take an X-ray spectrum of the source to study it, and to understand if it is really a point source or an enhancement of the pulsar nebula."101 ??— have pointed out that the inclusion of a black-bodyw componcut iu the fit of the ASCA GIS|SIS data of 3€58 vields ai dmaprovement of the X7. MA, \cite*{tsk00} have pointed out that the inclusion of a black-body component in the fit of the ASCA GIS+SIS data of 3C58 yields an improvement of the $\chi^2$.102NThey claim. jit the best-fit black-body component is responsible for ~ of the unabsorbed flux in the 10 keV of the whole remmaut. aud that it is the spectra signature of the ceutral source.," They claim that the best-fit black-body component is responsible for $\sim 7$ of the unabsorbed flux in the 0.5-10 keV of the whole remnant, and that it is the spectral signature of the central source."103 It is also very important to assess the presence of a shell around the pulsu nebula. for it may give compclling constraints on the age of the remnant. the shock velocity aud the eusitv of the environment.," It is also very important to assess the presence of a shell around the pulsar nebula, for it may give compelling constraints on the age of the remnant, the shock velocity and the density of the environment."104 Iu the case of the S00 vr old 3€58 (as other plerious as well) it is expecte hat he main shock will encounter the stellar ejecta aiefor the interstellar medium (ISM) eiving rise o a limb brightened shell.," In the case of the $\sim 800$ yr old 3C58 (as other plerions as well), it is expected that the main shock will encounter the stellar ejecta and/or the interstellar medium (ISM) giving rise to a limb brightened shell."105 However. uo sien o τα shell was been detected at ceutimeter wavelcueths at distances ereater than 5’ from the core (22)).," However, no sign of a shell has been detected at centimeter wavelengths at distances greater than $5\arcmin$ from the core \cite{ra85}) )."106 However. ?? have inaeed the faint outer emission of the nebula at a distance )etwoeen aud |’ and have noticed hub brightening at several ocations.," However, \cite*{ra88} have imaged the faint outer emission of the nebula at a distance between and $4\arcmin$ and have noticed limb brightening at several locations."107 Iu this paper. we preseut a study of the data of 3C€58 obtained during the Calibration aud Performance Verification (Cal/PV) phase of tle mission.," In this paper, we present a study of the data of 3C58 obtained during the Calibration and Performance Verification (Cal/PV) phase of the mission."108atomic diffusion can lead to abundance anomalies on the PMS. and that neglecting its effects could have an impact on calibrating atmosphere models.,"atomic diffusion can lead to abundance anomalies on the PMS, and that neglecting its effects could have an impact on calibrating atmosphere models."109Disks around galactic black holes are formed by the accretion of matter with angular momentum.,Disks around galactic black holes are formed by the accretion of matter with angular momentum.110 These disks are opaque and emit locally thermal radiation of temperatures up to ~10’ K (?).., These disks are opaque and emit locally thermal radiation of temperatures up to $\sim10^{7}$ K \citep{shakura}.111 These disks cannot be responsible for the hard X-ray emission extending up to a few MeV detected from Cygnus X-1 and similar X-ray binaries and microquasars in the low-hard state., These disks cannot be responsible for the hard X-ray emission extending up to a few MeV detected from Cygnus X-1 and similar X-ray binaries and microquasars in the low-hard state.112" This finding and the presence in the spectrum of features like a broad iron Ko line and a hard X-ray bump, led to the idea that a corona of hot plasma might surround the black hole and part of the disk."," This finding and the presence in the spectrum of features like a broad iron $\alpha$ line and a hard X-ray bump, led to the idea that a corona of hot plasma might surround the black hole and part of the disk."113 Two-temperature models for this plasma were first suggested by ?.., Two-temperature models for this plasma were first suggested by \citet{shapiro}.114 In these types of models protons are much hotter than electrons (T;>> Τε)., In these types of models protons are much hotter than electrons $ T_{i}>>T_{e}$ ).115" Since the pressure is dominated by the protons, the disk inflates, the density drops, and there is a low rate of Coulomb energy exchange between protons and electrons, allowing the existence of a two-temperature plasma in a self-consistent way."," Since the pressure is dominated by the protons, the disk inflates, the density drops, and there is a low rate of Coulomb energy exchange between protons and electrons, allowing the existence of a two-temperature plasma in a self-consistent way."116 The Comptonization of soft photons results in a hard X-ray spectrum., The Comptonization of soft photons results in a hard X-ray spectrum.117" The model, however, is unstable to small perturbations in the ion temperature 7; (??).."," The model, however, is unstable to small perturbations in the ion temperature $T_{i}$ \citep{pringle,piran}."118" When the plasma density is very low, the protons are unable to transfer energy to the electrons."," When the plasma density is very low, the protons are unable to transfer energy to the electrons."119" If matter is advected into the black hole (???) or removed outward as a hot wind (?),, thermally stable solutions can be found."," If matter is advected into the black hole \citep{ichimaru,narayana,narayanb} or removed outward as a hot wind \citep{blandford01}, thermally stable solutions can be found."120" The geometry of the region with the hot plasma is not well-constrained, but a spherical region around the black hole is usually considered (e.g.,??).."," The geometry of the region with the hot plasma is not well-constrained, but a spherical region around the black hole is usually considered \citep[e.g.,][]{esin01,esin02}."121 The two-temperature plasma then forms a hot corona around the black hole., The two-temperature plasma then forms a hot corona around the black hole.122" In the different spectral states, the cold disk penetrates to different distances from the black hole."," In the different spectral states, the cold disk penetrates to different distances from the black hole."123" In the very state it goes all the way down to the last stable orbit (see ??,, for comprehensive reviews)."," In the very high-soft state it goes all the way down to the last stable orbit (see \citealt{narayan02,narayan03}, for comprehensive reviews)."124 The general view of a relatively low density hot corona and a cold accretion disk was presented by ?.., The general view of a relatively low density hot corona and a cold accretion disk was presented by \citet{bisnovatyi}.125 'The mechanism for heating the corona may be magnetic reconnection of field loops emerging from the disk (?).., The mechanism for heating the corona may be magnetic reconnection of field loops emerging from the disk \citep{galeev}.126" Violent reconnection may lead to plasma motions and collisions, with shock formation."," Violent reconnection may lead to plasma motions and collisions, with shock formation."127" A non-thermal particle population might then arise in the corona as the result of diffusive shock acceleration (e.g.,?).."," A non-thermal particle population might then arise in the corona as the result of diffusive shock acceleration \citep[e.g.,][]{spruit}."128 The effects of a non-thermal population of electrons in a hot corona were considered by ? and more recently by ? and ?.., The effects of a non-thermal population of electrons in a hot corona were considered by \citet{kusunose} and more recently by \citet{belmont} and \citet{vurm}.129 The results of the injection of non-thermal protons and secondary pions and muons in a magnetized corona has not been comprehensively studied so far., The results of the injection of non-thermal protons and secondary pions and muons in a magnetized corona has not been comprehensively studied so far.130 The contributions from the transient particles can be important at high energies., The contributions from the transient particles can be important at high energies.131 The emerging emission from all non-thermal processes may in principle be detectable by future Cherenkov telescope arrays such as CTA or AGIS., The emerging emission from all non-thermal processes may in principle be detectable by future Cherenkov telescope arrays such as CTA or AGIS.132" Hence, high-energy gamma-ray astronomy can provide a tool to probe the non-thermal particle content of hot coronae around black holes."," Hence, high-energy gamma-ray astronomy can provide a tool to probe the non-thermal particle content of hot coronae around black holes."133" In this paper, we present detailed calculations of the radiative output of non-thermal particles in a simplified model of magnetized corona."," In this paper, we present detailed calculations of the radiative output of non-thermal particles in a simplified model of magnetized corona."134 The existence of the corona is assumed and the effect of injection of both relativistic protons and electrons are considered., The existence of the corona is assumed and the effect of injection of both relativistic protons and electrons are considered.135 The distributions of all relevant secondary particles are estimated and their radiative output computed., The distributions of all relevant secondary particles are estimated and their radiative output computed.136 The coronal matter and radiative fields are considered as targets for the populations of relativistic particles., The coronal matter and radiative fields are considered as targets for the populations of relativistic particles.137 The internal absorption of gamma-rays is calculated and the spectral energy distributions of different models are presented., The internal absorption of gamma-rays is calculated and the spectral energy distributions of different models are presented.138" The result is a self-consistent treatment of the non-thermal processes in the sense that once the medium is fixed in each model, we solve the transport equations for all type of particles and use the obtained particle distributions to estimate the non-thermal radiation."," The result is a self-consistent treatment of the non-thermal processes in the sense that once the medium is fixed in each model, we solve the transport equations for all type of particles and use the obtained particle distributions to estimate the non-thermal radiation."139 The structure of the paper is as follows., The structure of the paper is as follows.140" In Sect. ??,,"," In Sect. \ref{scenario},"141 we outline the basic scenario that is discussed in the paper., we outline the basic scenario that is discussed in the paper.142 Section ?? deals with particle acceleration and losses in the coronal environment., Section \ref{losses} deals with particle acceleration and losses in the coronal environment.143 The maximum energy for the different particles is determined., The maximum energy for the different particles is determined.144" In Sect. ??,,"," In Sect. \ref{SEDs},"145" the radiation is calculated and the spectral energy distributions are presented, for different sets of parameters."," the radiation is calculated and the spectral energy distributions are presented, for different sets of parameters."146 Section ?? presents an application to Cygnus X-1., Section \ref{Cyg} presents an application to Cygnus X-1.147 We close with a, We close with a148requires a consistent excitation temperature of ED KI. which is likely the temperature of the outermost laver of the cloud.,"requires a consistent excitation temperature of $\sim$ K, which is likely the temperature of the outermost layer of the cloud."149 The00. aand llines are peaked at the velocity of the ddip GQuarked as a dashed vertical line in ref20231-spec-alltinh)). with a oofgus. very close to that of our lines.," The, and lines are peaked at the velocity of the dip (marked as a dashed vertical line in \\ref{20231-spec-all-tmb}) ), with a of, very close to that of our lines."150" From the ratio of peak temperatures of the aaud lines. assuming a ΟΣΟΙ abundance ratio of Το (Wilson Rood 1991)). we find an LTE excitation enperature of 1011 for he J = 21 aud Kk for he J = 32 enüssion. aud moderate optical depths of 196 aud 0.5 at the peak velocity for the — 2 1aud 32 ransitions ofΟ., respectively."," From the ratio of peak temperatures of the and lines, assuming a ] abundance ratio of 7.5 (Wilson Rood \cite{Wilson94}) ), we find an LTE excitation temperature of K for the $J$ = 2–1 and K for the $J$ = 3–2 emission, and moderate optical depths of 0.96 and 0.8 at the peak velocity for the $J$ = 2–1 and 3–2 transitions of, respectively."151 We adopt au excitation eniperature of LOWS for the ambicut molecular eas in he following calculations., We adopt an excitation temperature of K for the ambient molecular gas in the following calculations.152 Estimated frou the ratio of integrated intensities of παςCHO.. we find 7~0.5 for the J = 32 aud 21 line xofiles of CTO.," Estimated from the ratio of integrated intensities of and, we find $\bar{\tau}$ $\sim$ 0.5 for the $J$ = 3–2 and 2–1 line profiles of ."153".. After applying a 7. correction Quultiply wea factor of τό.« 7T)) we estimate LTE ccoluin deusities of 1.11016 and οσι for the inner 22"". and EY of the cloud."," After applying a $\tau$ –correction (multiply by a factor of $\bar{\tau}/(1-e^{-\bar{\tau}}$ )), we estimate LTE column densities of $\times10^{16}$ and $\times10^{15}$ for the inner $''$ and $''$ of the cloud."154 These cad to. self-consisteut fractional abundances οἱ CHOJ[/TIS[]|—1.5 410 * aud 1.2410*. which ave in eood aerecineut with the ‘typical’ value of 410[ (Frevking et al. 1982)).," These lead to self-consistent fractional abundances of $\sim$ $\times$ $^{-7}$ and $\times10^{-7}$, which are in good agreement with the `typical' value of $\times10^{-7}$ (Frerking et al. \cite{Frerking82}) )."155 BOO and wwere also mappedο in the central part of the northeru core (see panels aud of L))., $^{13}$ CO and were also mapped in the central part of the northern core (see panels and of \ref{20231-allother}) ).156 lis believed to be optically thin aud therefore cau be used for mass estimation., is believed to be optically thin and therefore can be used for mass estimation.157" The peak LTE colhuun denusitv of iis caleulated to be «101!ciusq., which gives a fractional aabundance of Lb.10"," The peak LTE column density of is calculated to be $\times10^{14}$, which gives a fractional abundance of $\times10^{-8}$."158 Using the integrated cussion over the mapped region. we estimate a quiescent molecular cloud mass associated with eecnmissionu to be 50solanass.. comparable to the mass derived from NIL;.," Using the integrated emission over the mapped region, we estimate a quiescent molecular cloud mass associated with emission to be $\sim$, comparable to the mass derived from ."159. Note that this mass ds onlv a lower linut due to the incompleteness of the map., Note that this mass is only a lower limit due to the incompleteness of the map.160 The deconvolyed size estimated from the ceelission is about 107 by 75” (Q2ppe by ppc). slightly larger than those estimated from the 8STOa42 dust Cluission and the (1.1) line emission ofNIT;.," The deconvolved size estimated from the emission is about $''$ by $''$ pc by pc), slightly larger than those estimated from the $\mu$ m dust emission and the (1,1) line emission of."161. Droad-line wing emission has been detected in both CO J=2 land 32 transitions toward the ceutral region iu Las70., Broad-line wing emission has been detected in both CO $J$ = 2–1 and 3–2 transitions toward the central region in 870.162 The wwing cussion. determined from a comparison of aand pprofiles. is defined w velocities redder than 9 oor bluer than 3," The wing emission, determined from a comparison of and profiles, is defined by velocities redder than 9 or bluer than 3."163" Simce CO J=2 1 and 32 laps of the outflowing material show very similar bipolar structures, we present iu rof20231-co-bipolar oulv the higher augublu resolution CO J=32 data."," Since CO $J$ =2–1 and 3–2 maps of the outflowing material show very similar bipolar structures, we present in \\ref{20231-co-bipolar} only the higher angular resolution CO $J$ =3–2 data."164" The bluc- (.12 to kimns)) aud the red-shifted (9 to kums)) lobes are shown iu solid and dashed coutours. respectively,"," The blue- (–12 to ) and the red-shifted (9 to ) lobes are shown in solid and dashed contours, respectively."165 Note hat the iuteeral of the redshüfted due cussion was dutentionallv truncated to avoid contanination frou a separate velocity component at aboutjus... which appears in three attached spectra at the right side of ref20231-co-bipolar..," Note that the integral of the redshifted wing emission was intentionally truncated to avoid contamination from a separate velocity component at about, which appears in three attached spectra at the right side of \\ref{20231-co-bipolar}."166 Being centered on 1220231. the outflow lobes are asvuuuetric and show some evidence of chuupiness. especially in the red lobe.," Being centered on 20231, the outflow lobes are asymmetric and show some evidence of clumpiness, especially in the red lobe."167 There is some overlap between re and blue-shüfted. enission., There is some overlap between red and blue-shifted emission.168 Interestingly. close to the southern dust coutiuuun peak. a pair of weak πιο aud red-shifted lobe is also detected. indicative of οσοας star formation activity in this regiou too.," Interestingly, close to the southern dust continuum peak, a pair of weak blue- and red-shifted lobe is also detected, indicative of ongoing star formation activity in this region too."169 Velocity chamuel maps (Fie.6)) and a position. velocity map along the declination axis (Fie.7)) support this view., Velocity channel maps \ref{20231-all-chmap}) ) and a position velocity map along the declination axis \ref{20231-co32-pv})) support this view.170 The blue-shifted lobe is. however. not fully covered by ourmap.," The blue-shifted lobe is, however, not fully covered by ourmap."171 preseuts a series of velocity maps iu steps of laus., \\ref{20231-all-chmap} presents a series of velocity maps in steps of .172 We have skipped the emission between, We have skipped the emission between173naenitude of reflection is from BeppoSAX observations.,magnitude of reflection is from BeppoSAX observations.174 For the two points with ower frequency. we had simultancous RATE iud BeppoSAN observations.," For the two points with lower frequency, we had simultaneous RXTE and BeppoSAX observations."175 For the upper two points. we inferred the ΟΡΟ frequency based on the QPO frequency versus photon index relation from Ἱναανο ct ((1998) aud the photon iudex ueasured with BeppoSAN and allowing for a systematic offset iun photon indices )etween BeppoSAX and RNTE measured using simultaneous obscrvatious.," For the upper two points, we inferred the QPO frequency based on the QPO frequency versus photon index relation from Kaaret et (1998) and the photon index measured with BeppoSAX and allowing for a systematic offset in photon indices between BeppoSAX and RXTE measured using simultaneous observations."176 The arge error bars for these two points are due to the uncertainty in this extrapolation., The large error bars for these two points are due to the uncertainty in this extrapolation.177 The QPO frequency appears correlated with the magnitude of reflection., The QPO frequency appears correlated with the magnitude of reflection.178 The correlation is consistent with that expected if the QPO frequeney is determined by the orbital requencv at the iuuer edee of the disk aud the variation iu reflection is due to changes in the mnoer disk radius., The correlation is consistent with that expected if the QPO frequency is determined by the orbital frequency at the inner edge of the disk and the variation in reflection is due to changes in the inner disk radius.179 Tsugeest the following plivsical picture to explain the correlations of ΟΡΟ frequency with spectral state and magnitude of reflection presented iu the previous sections., I suggest the following physical picture to explain the correlations of QPO frequency with spectral state and magnitude of reflection presented in the previous sections.180 Mass accretion can occur in ueutron star x-ray binaries both through the accretion disk aud racially (c.g. Cohosh Laub 1978)., Mass accretion can occur in neutron star x-ray binaries both through the accretion disk and radially (e.g. Ghosh Lamb 1978).181 The total mass accretion rate. disk plus radial. determines the total huninositv of the svstem.," The total mass accretion rate, disk plus radial, determines the total luminosity of the system."182 The mass accretion rate through the disk determines the radius of the inner edge of the disk aud. via the dependence of the overall προς on the soft photon fiux cmitted from the disk. the spectral state of the svstem.," The mass accretion rate through the disk determines the radius of the inner edge of the disk and, via the dependence of the overall spectrum on the soft photon flux emitted from the disk, the spectral state of the system."183 The QPO frequeney is determined by the radius of the inner edge of the disk., The QPO frequency is determined by the radius of the inner edge of the disk.184 The data presented above are fully cousisteut with this picture., The data presented above are fully consistent with this picture.185 To answer the questions posed earlier: The existence of the mareially stable orbit will have a strong effect on the configuration of the accretion disk ucar the neutron star as the lack of stable orbits awards of the mareially stable orbit iaplies that a stable disk can not exist iu that region., To answer the questions posed earlier: The existence of the marginally stable orbit will have a strong effect on the configuration of the accretion disk near the neutron star as the lack of stable orbits inwards of the marginally stable orbit implies that a stable disk can not exist in that region.186 The inner radii of disks around neutron stars appear to be variable., The inner radii of disks around neutron stars appear to be variable.187 The truncation of the disk may be caused. by the neutron star maguetic field. by radiatiou forces acting on the disk. or by a disk instability.," The truncation of the disk may be caused by the neutron star magnetic field, by radiation forces acting on the disk, or by a disk instability."188 In general. the inner disk radius decreases with increasing mass accretion rate through the disk.," In general, the inner disk radius decreases with increasing mass accretion rate through the disk."189 The mareially stable orbit, The marginally stable orbit190oof material (Actasefal.198s:Momoseal...1998).. which produces ~30L.. iin luminous ouput (Ixeeue&Masso11990).,"of material \citep{ALS88,Mom98}, which produces $\sim$ in luminous output \citep{KeeMas90}."191. We present a numerical sinuulatiou of a binary star/disk+star/cisk system using a two dimensional Grey) S9moothec Particle Hydrovnamic (SPH) code.," We present a numerical simulation of a binary $+$ star/disk system using a two dimensional $x,y$ ) Smoothed Particle Hydrodynamic (SPH) code."192 The citmeusious of the disks aud semi-major axis of the binaΝ are chosen to |ye πας to the iuner core region of5., The dimensions of the disks and semi-major axis of the binary are chosen to be similar to the inner core region of.193. Iu the absence ol strong coustraints on the constituents of the binary (e.g. tlie masses of the two stars). we choose 1o set up a binary system consisting of identical components. obtained by setting up a single system in isolation. then duplicating it exactly.," In the absence of strong constraints on the constituents of the binary (e.g. the masses of the two stars), we choose to set up a binary system consisting of identical components, obtained by setting up a single system in isolation, then duplicating it exactly."194" We assume each star and disk lave mass AM,=0.5M.. aan Aj)=0.05M.... respectively."," We assume each star and disk have mass $M_*=0.5$ and $M_D=0.05$, respectively."195 TThe disk radius is set to Rp—15 AU which. for a semi-major axis of a=50 AU. is compa‘able tot he largest stable streamline (Paczyvüski1977).," The disk radius is set to $R_D=15$ AU which, for a semi-major axis of $a=50$ AU, is comparable to the largest stable streamline \citep{Pac77}."196". The mass aud temperature of the disk"" are distributedη. accordiηο tor oE7Zand pU?M power laws respectivev.", The mass and temperature of the disk are distributed according to $r^{-3/2}$ and $r^{-1/2}$ power laws respectively.197 The absolte scale of each power law is cleteruined from the disk mass. the racdia dimensious of tje clisk a e condition that the Toomre stability parameter. Q. is no sinaller μαι 711.5 over tlie eutir isk.," The absolute scale of each power law is determined from the disk mass, the radial dimensions of the disk and the condition that the Toomre stability parameter, $Q$, is no smaller than 1.5 over the entire disk."198 Tlis value ensures that the simulation begins in a state mareinally stable agaiust he grow [ spiral structure. so that we do not. accidently “discover a colapsec object early in the evolution which iu reality is an artifact of our initial couclition.," This value ensures that the simulation begins in a state marginally stable against the growth of spiral structure, so that we do not accidently `discover' a collapsed object early in the evolution which in reality is an artifact of our initial condition."199 Bohi density aud temperature are free to vary in time aud space. so the initial condition will uot prevent sdia structure growth or fragmentation. if the evolution leads to such.," Both density and temperature are free to vary in time and space, so the initial condition will not prevent spiral structure growth or fragmentation, if the evolution leads to such."200 The gas is set up ou circular orbits around the star so that pressure aud gravitational forces exactly balance centrifugal forces., The gas is set up on circular orbits around the star so that pressure and gravitational forces exactly balance centrifugal forces.201 Raclia motion is zero., Radial motion is zero.202 The maeuitucdes of the pressure aud sell-gravitational forces are small compared to the stellar gravity. so the clisk is nearly. Ixeplerian in character.," The magnitudes of the pressure and self-gravitational forces are small compared to the stellar gravity, so the disk is nearly Keplerian in character."203 Aproximately 60000 equal mass particles are set ou a series of couceltric rings arould the star I asiiele. star/disk system. then duplicated. bringing the total number of particles to ~ 120000.," Approximately 60000 equal mass particles are set on a series of concentric rings around the star in a single, star/disk system, then duplicated, bringing the total number of particles to $\sim$ 120000."204 The two stars aud disks are offset equal cistauces in tlie +:r and —.r directious., The two stars and disks are offset equal distances in the $+x$ and $-x$ directions.205 We define he binary semi-major axis to be a=50 AU. similar to5.," We define the binary semi-major axis to be $a=50$ AU, similar to."206. Only weak constraiuts on eccentricity exist in5.. prisjarilv cosisting of the sizes of the observed disks: eeceutricities larger han e=0.3) would lead ο rapid Roche lobe overflow.," Only weak constraints on eccentricity exist in, primarily consisting of the sizes of the observed disks: eccentricities larger than $e=0.3$ would lead to rapid Roche lobe overflow."207 We set e=0.) to be the initial value in this simulation., We set $e=0.3$ to be the initial value in this simulation.208 The system is a apoapse at time /=0 with the orbital velocities «leliued by approximating each stard-disk system as a poiut mass. so that the orbit determination reduces to he solution of the two body problem.," The system is at apoapse at time $t=0$ with the orbital velocities defined by approximating each $+$ disk system as a point mass, so that the orbit determination reduces to the solution of the two body problem."209 The clisks are self eravitatiug aid each star is 11ocleled as a polit mass free to move in response O gravitational forces [rom the res of tlie system., The disks are self gravitating and each star is modeled as a point mass free to move in response to gravitational forces from the rest of the system.210 The stellar gravitational forces are calculated ine a Pluumer potentla nith a softeiine raclits of 0.2 AU. which also serves as an accretion πα.," The stellar gravitational forces are calculated using a Plummer potential with a softening radius of 0.2 AU, which also serves as an accretion radius, $r_{acc}$."211 SPH particles ith trajectories that pass closer than rgo lO a star are absorbed. aud he starslass alkl momel1 increase accordingly.," SPH particles with trajectories that pass closer than $r_{acc}$ to a star are absorbed, and the star's mass and momentum increase accordingly."212“ The tlermodsynamic evoltion is idettical to that described in Nelsouefad.(2000)., The thermodynamic evolution is identical to that described in \citet{DynamII}.213. Thermal enerey is acldecdl to the gas «ue to active hycrodynuatHe processes usiug au artificial viscosity scheme. which approximatelvy mocles shocks ancl ttrbulence.," Thermal energy is added to the gas due to active hydrodynamic processes using an artificial viscosity scheme, which approximately models shocks and turbulence."214 This beatingOm is roughlyOm equivalent in magnitudee, This heating is roughly equivalent in magnitude215To study the nonlinear evolution of these eigenmodes. we considered the ten most rapidly growing ones. and adjusted the energy in each to be either or of the energy in the background field Bo.,"To study the nonlinear evolution of these eigenmodes, we considered the ten most rapidly growing ones, and adjusted the energy in each to be either or of the energy in the background field ${\bf B}_0$."216 In total. the energy that 1s initially in the perturbations is therefore either or of the energy 1n the background field.," In total, the energy that is initially in the perturbations is therefore either or of the energy in the background field."217 These two setups. background field plus either small or large perturbations. were then used as the initial conditions m the original. nonlinear Eq. (1)).," These two setups, background field plus either small or large perturbations, were then used as the initial conditions in the original, nonlinear Eq. \ref{eq:A}) )."218 Both simulations were performed at resolutions of 128? and 256. with no difference in the results.," Both simulations were performed at resolutions of $128^3$ and $256^3$, with no difference in the results."219 Figure 2 shows the results for the small perturbations. energy in each of the top ten eigenmodes.," Figure \ref{small} shows the results for the small perturbations, energy in each of the top ten eigenmodes."220 At very early times. the energy in these modes does indeed grow. and at the rates predicted by the linear stability analysis.," At very early times, the energy in these modes does indeed grow, and at the rates predicted by the linear stability analysis."221 However. this phase is so short. only up to’=0.01. that there is virtually no growth in this time: with growth rates of ~0.4 on this Hall timescale. the perturbations grow by only a factor of exp(0.01-0.4)=1.004.," However, this phase is so short, only up to $t'\approx0.01$, that there is virtually no growth in this time; with growth rates of $\sim0.4$ on this Hall timescale, the perturbations grow by only a factor of $\exp(0.01\cdot0.4)=1.004$."222 One could of course make this linear growth phase much longer. simply by assuming the initial perturbations to be smaller.," One could of course make this linear growth phase much longer, simply by assuming the initial perturbations to be smaller."223 However. as soon as they approach the ~15€ energy level. the linear growth phase ends. and one is once again in the regime shown here.," However, as soon as they approach the $\sim1$ energy level, the linear growth phase ends, and one is once again in the regime shown here."224 As indicated in Fig. 2..," As indicated in Fig. \ref{small},"225 by //«0.025. the nonlinear interactions among these modes are clearly beginning to spread the energy to different &..κι combinations.," by $t'\approx0.025$, the nonlinear interactions among these modes are clearly beginning to spread the energy to different $k_x, k_y$ combinations."226" This is most easily seen in the Κι spectrum. where the &,=10 initial condition generates higher harmonies at e.g."," This is most easily seen in the $k_y$ spectrum, where the $k_y\approx10$ initial condition generates higher harmonics at e.g.,"227of the fast-magnetosonic point as follows. We note that this critical point exists only if £2>1—(1/27). while the allowed range is ]«ry<x. depending crucially on the difference £2—1.,"of the fast-magnetosonic point as follows, We note that this critical point exists only if $\xi_{\rm F}^{2} > 1 - (1/E^{2/3})$, while the allowed range is $1 < x_{\rm F} < \infty$, depending crucially on the difference $\xi_{\rm F}^{2}-1$."228 On the other hand. for the value of Mg at the fast-magnetosonic point we obtain To show the physical implication of equation (26)). we consider the specific magnetic energv {ο al a radius οδν1 bevond the light evlinder.," On the other hand, for the value of $M^{2}_{\rm F}$ at the fast-magnetosonic point we obtain To show the physical implication of equation \ref{M/x}) ), we consider the specific magnetic energy $E_{m}$ at a radius $x\gg1$ beyond the light cylinder."229 From equations (2)) aud (6)) we obtain approximately where we have introduced (he quantity AF defined by M?=AL>/3?., From equations \ref{menergy}) ) and \ref{toroidal}) ) we obtain approximately where we have introduced the quantity $\mm^{2}$ defined by $ \mm^{2}\equiv M^{2}/x^{2} $.230" Then the ratio of the specilic kinetic energv Fy,=E—E, to E, is given by which implies (hat M? is an indicator of the conversion of the huge magnetic energv into (he kinetic energy for outflows propagating to a radius cc1. (", Then the ratio of the specific kinetic energy $E_{k}=E-E_{m}$ to $E_{m}$ is given by which implies that $\mm^{2}$ is an indicator of the conversion of the huge magnetic energy into the kinetic energy for outflows propagating to a radius $x\gg 1$. (231The term AP corresponds {ο the inverse of the magnetization parameter c in some wind models: see. e.g. Michel and Camenzind(1936) for the radial wind. ancl Begelman&Li(1994). ancl Takahashi&Shibata(1993) for non-radial winds.),"The term $\mm^2$ corresponds to the inverse of the magnetization parameter $\sigma$ in some wind models; see, e.g, \cite{mc69} and \cite{cam86} for the radial wind, and \cite{bl94} and \cite{ts98} for non-radial winds.)"232 At the fast-magnetosonic point. however. we obtain from equation (26)) which is a generic result independent ofa lield configuration YC.Z) of highly relativistic outflows.," At the fast-magnetosonic point, however, we obtain from equation \ref{M/x}) ) which is a generic result independent of a field configuration $\Psi(R,Z)$ of highly relativistic outflows."233 It is clear that the energy conversion is still inefficient at the [ast-magnetosonic point., It is clear that the energy conversion is still inefficient at the fast-magnetosonic point.234 Then. we consider plasma acceleration of trans-[ast-iagnetosonic outflows propagating ab a radius àX1 bevond the critical point. where we have approximately," Then, we consider plasma acceleration of trans-fast-magnetosonic outflows propagating at a radius $x\gg1$ beyond the critical point, where we have approximately"235fformation.,formation.236samples are dominated by late-twpes. whereas. earlv-tvpes are the most common galaxies in bright samples.,"samples are dominated by late-types, whereas early-types are the most common galaxies in bright samples."237 Similar trends were found. for. galaxies labelled by morphological tvpe in the SSRS2 survey by Marzke (1998)., Similar trends were found for galaxies labelled by morphological type in the SSRS2 survey by Marzke (1998).238 We find that the change in the mix of spectral types with luminosity is not the main cause for the increase in the clustering streneth of the full sample with Iuminositv., We find that the change in the mix of spectral types with luminosity is not the main cause for the increase in the clustering strength of the full sample with luminosity.239 ‘To support this assertion. we plot in Fig.," To support this assertion, we plot in Fig."240" 10. the variation of clustering strength with luminosity normalized. for spectral class. to the clustering strength of a fiducial sample of eealaxies. the sample which covers the magnitude range 19.5»M,Slog,h220.5."," \ref{fig:bl} the variation of clustering strength with luminosity normalized, for spectral class, to the clustering strength of a fiducial sample of galaxies, the sample which covers the magnitude range $-19.5\,\ge\,M_{b_{\rm J}}-5\log_{10}\,h\,\ge\,-20.5$."241 For a galaxy sample with best fitting correlation function parameters ry and >! we define the relative bias with respect to the ssaimple of the same type by where ry and. ο are the best fitting power-law parameters for the fiducial sample.," For a galaxy sample with best fitting correlation function parameters $r^{i}_{0}$ and $\gamma^{i}$, we define the relative bias with respect to the sample of the same type by where $r_{0}$ and $\gamma$ are the best fitting power-law parameters for the fiducial sample."242 In Fig. 10..," In Fig. \ref{fig:bl},"243 we plot the relative bias evaluated at a fixed. scale. r=4895.Mpc.. which is the correlation length of the reference sample for all g--classified galaxies.," we plot the relative bias evaluated at a fixed scale, $r = 4.89$, which is the correlation length of the reference sample for all -classified galaxies."244 A scale dependence in Eq., A scale dependence in Eq.245 9. arises if the slopes of the real space correlation functions are cillerent for the galaxy samples being compared., \ref{eq:bias} arises if the slopes of the real space correlation functions are different for the galaxy samples being compared.246 In. practice. the term ag is close to unity for the samples considered.," In practice, the term $r^{\gamma-\gamma_{i}}$ is close to unity for the samples considered."247 The dashed line shows a fit to the bias relation defined by the open svmbols., The dashed line shows a fit to the bias relation defined by the open symbols.248 The solid line shows the effective bias relation obtained by(2001)... which is defined in a slightly dilferent way to the ellective bias computed here.," The solid line shows the effective bias relation obtained by, which is defined in a slightly different way to the effective bias computed here."249 From Fig. 10.," From Fig. \ref{fig:bl},"250 we see that the trend. of increasing clustering strength with luminosity in both spectral classes is very similar for galaxies brighter than £L>0.5L*., we see that the trend of increasing clustering strength with luminosity in both spectral classes is very similar for galaxies brighter than $L>0.5L^{\star}$.251 At the xiehtest Luminosity. corresponding to Εν the clustering amplitude is a factor of9.5 times greater than at L.," At the brightest luminosity, corresponding to $\sim\,4 L^{\star}$, the clustering amplitude is a factor of $2-2.5$ times greater than at $L^{\star}$."252 Ehis increase is much larger than the offset in the relative bias actors of carly and late types at any. given luminosity., This increase is much larger than the offset in the relative bias factors of early and late types at any given luminosity.253 We conclude that the change in correlation length with absolute magnitude found by Norberg (2001) is primarily a uminositv effect. rather than a rellection of the change in he mix of spectral types with lumainosity., We conclude that the change in correlation length with absolute magnitude found by Norberg (2001) is primarily a luminosity effect rather than a reflection of the change in the mix of spectral types with luminosity.254 Benson (2001) showed that a dependence: of clustering strength on luminosity is expected in hierarchical clustering. cold. dark matter universes because of the preferential formation of the brightest galaxies in the most massive. strongly clustered dark halos.," Benson (2001) showed that a dependence of clustering strength on luminosity is expected in hierarchical clustering cold dark matter universes because of the preferential formation of the brightest galaxies in the most massive, strongly clustered dark halos."255 Phe close connection between the spectral characteristics of galaxies and. their clustering properties discussed in this paper provides further evidence that the galaxy type is also related to the mass of the halo in which galaxy formis., The close connection between the spectral characteristics of galaxies and their clustering properties discussed in this paper provides further evidence that the galaxy type is also related to the mass of the halo in which galaxy forms.256 The 2dEGIS is being carried out using the 2 degree field facility on the 3.9m AngloXXustralian. Telescope (AAT)., The 2dFGRS is being carried out using the 2 degree field facility on the 3.9m Australian Telescope (AAT).257 We thank all those involved. in the smooth running and continued success of the 2dE and the AAT., We thank all those involved in the smooth running and continued success of the 2dF and the AAT.258 We thank the referee. Dr. J. Loveday. for producing a speedy ancl helpful report.," We thank the referee, Dr. J. Loveday, for producing a speedy and helpful report."259 PN is supported by the Swiss National Science Foundation and an ORS award. and CMD acknowledges the receipt of a Roval Society University Research Fellowship.," PN is supported by the Swiss National Science Foundation and an ORS award, and CMB acknowledges the receipt of a Royal Society University Research Fellowship."260 This work was supported in part by a PPARC rolling erant at Durham., This work was supported in part by a PPARC rolling grant at Durham.261the process can contribute to nuclei made by the s-process that are unshielded against 2 decay of more neutron-rich isobars. so loo can the v—rp process considered here contribute to s-nuclei (hat are unshielded on the proton-rich side.,"the $r$ -process can contribute to nuclei made by the $s$ -process that are unshielded against $\beta$ decay of more neutron-rich isobars, so too can the $\nu-rp$ process considered here contribute to $s$ -nuclei that are unshielded on the proton-rich side."262 That is. in addition to nuclei that are designated as 77r.5. there may also be nuclei one should consider as 7p.s.," That is, in addition to nuclei that are designated as $r,s$ ”, there may also be nuclei one should consider as $p,s$ ”."263 The fourth stage only occurs in the most extreme situation where the number of neutrons produced by neutrinos is quite large compared with (he number of seed nuclei., The fourth stage only occurs in the most extreme situation where the number of neutrons produced by neutrinos is quite large compared with the number of seed nuclei.264 Then (n.p) reactions not only carry (he flow at low temperature back to the vallev of beta stability. but (n.5) reactions carry it bevond -chart. even in (he presence of a large abundance of [ree protons.," Then (n,p) reactions not only carry the flow at low temperature back to the valley of beta stability, but $\gamma$ ) reactions carry it beyond -, even in the presence of a large abundance of free protons."265 This is a novel version of the r-process that actually works best when (he abundance is large bul the temperature too low for proton addition., This is a novel version of the $r$ -process that actually works best when the abundance is large but the temperature too low for proton addition.266 The protons are just a source of neutrons., The protons are just a source of neutrons.267 The most interesting part of the uucleosvuthesis occurs during Che later stages of the outflow as the material cools., The most interesting part of the nucleosynthesis occurs during the later stages of the outflow as the material cools.268 In the absence of an important neutrino flux the final isotopic vields ave determined by an interplay between (p.5). (5.p) and 9 processes as well as details of how these reactions fall out of equilibrium.," In the absence of an important neutrino flux the final isotopic yields are determined by an interplay between $({\rm p},\gamma)$, $(\gamma,{\rm p})$ and $\beta^+$ processes as well as details of how these reactions fall out of equilibrium."269 When neutrino capture on [ree protons is important. nuclei are pushed to higher isospin and mass via (n.p) and (1.5) reactions.," When neutrino capture on free protons is important, nuclei are pushed to higher isospin and mass via ${\rm (n,p)}$ and $\gamma$ ) reactions."270 As a Bust approximation neutrinos will be important if they create an appreciable nunmber of neutrons per heavy nucleus., As a first approximation neutrinos will be important if they create an appreciable number of neutrons per heavy nucleus.271" The ratio of created free neutrons {ο heavy nuclei is where Xj, is the mass fraction of elements heavier than à. particles and ο is an elective average atomic number.", The ratio of created free neutrons to heavy nuclei is where $X_{\rm heavy}$ is the mass fraction of elements heavier than $\alpha$ particles and $\bar{A}$ is an effective average atomic number.272 In eq., In eq.273 2 is (he net number of neutrinos captured per free proton at temperatures smaller than about 3+ 10?K. Here ↕⊳∖⇁⊔∐↲↕⋅≀↧↴∩↲≀↧↴↥∖∖⊽∐↕≺∢↥⊔↲≀↧↴≺∢∐∐⋅≼↲≼↲↕↽≻↕⋅∪↥∪∐≺∢≀↧↴↕↽≻⊓∐⋅≼↲⋟∖⇁↗≐∕↙⋅⋝∖⊽⋜⋝≼↽≥, \ref{yneq} is the net number of neutrinos captured per free proton at temperatures smaller than about $3\cdot 10^9$ K. Here is the rate at which each free proton captures $\bar{\nu}_e$ 's \citep{qia96}.274↕≀↧↴∐≪↽, In eq.275∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."276∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."277∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."278∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."279∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."280∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."281∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."282∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."283∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."284∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."285∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."286∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."287∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."288∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."289∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."290∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."291∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."292∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."293∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕↽," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."294∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕↽≻," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."295∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕↽≻↥," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."296∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕↽≻↥∐," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."297∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕↽≻↥∐↲," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."298∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕↽≻↥∐↲↕," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."299∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕↽≻↥∐↲↕⋅," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."300∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕↽≻↥∐↲↕⋅≼," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."301∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕↽≻↥∐↲↕⋅≼↲," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."302∖↽∖∖⊽∪∪⋟∖⇁↥≼↲∡∖⇁⊥≤∍≤∍≺≨⇄⋝⋅⋅↕∐≼↲≺⇂⋅∔ ∠∣↴↴↕⋟∖⊽⊔∐↲↥∏∐↓↕∐∪⋟∖⊽∐⋡∖↽∪↓⋟≼↲↥≼↲≺∢⊔⋅∪∐≀↕↴∐∐−∐≼↲⋯↕⋅↕∐∪⋟∖⊽⋅⊺∣↴↴↕⋟∖⇁≀↕↴∐≼↲∐⋡≼↲≺∢∐∖↽≼↲∩↲∐↓↕↽≻≼↲↕⋅≀↕↴⊓∐⋅≼↲↓⋟∪↕⋅⊔∐↲⋟∖⊽≼↲ ∐≼↲⋯↕⋅↕∐∪⋟∖⊽≀↕↴∐≼⇂∣⋮↕⋟∖⊽⊔∐↲↕⋅≀↧↴≼∐∏⋟∖⊽∪↓⋟⊔∐↲∐⋯∩↲↕⋅↕≀↧↴↥∐⋅∪∐↕⊔∐↲∐≼↲∏⊔⋅↕∐∪⋟∖⊽↕↽≻↥∐↲↕⋅≼↲⋅," \ref{lambdanu} $L_{\bar{\nu}_e}$ is the luminosity of electron anti-neutrinos, $T_{\bar{\nu}_e}$ is an effective temperature for these neutrinos and $r$ is the radius of the material from the neutrino sphere."3032007).. then black holes grew fastest at that time ancl so activity in galactic nuclei may have been greatest. at. hieh redshift.,", then black holes grew fastest at that time and so activity in galactic nuclei may have been greatest at high redshift."304 Llowever. periods of intense activity in à galactic nucleus could also arise at. lower redshift. due to mergers between gas-rich galaxies (e.g.Hopkinsetal.2005). or when a large reservoir of cold gas builds up in the galactic disk (Ixormendy&Ixennicutt2004:Ixaullmannetal.2007).," However, periods of intense activity in a galactic nucleus could also arise at lower redshift, due to mergers between gas-rich galaxies \citep[e.g.][]{b43} or when a large reservoir of cold gas builds up in the galactic disk \citep{b24,b40}."305. The raw material lor accretion onto the black hole is eas and dust in the galactic nucleus., The raw material for accretion onto the black hole is gas and dust in the galactic nucleus.306 How much gas and dust there is in the galactic nucleus depends on the local rate of formation of massive stars (Ciotti&Ostriker2007) and on mechanisms driving gas and dust into the nucleus rom elsewhere in the galaxy., How much gas and dust there is in the galactic nucleus depends on the local rate of formation of massive stars \citep{b25} and on mechanisms driving gas and dust into the nucleus from elsewhere in the galaxy.307 Mechanisms driving material into the galactic nucleus from the outside could be internal or external to the galaxy., Mechanisms driving material into the galactic nucleus from the outside could be internal or external to the galaxy.308 Internal mechanisms involve bars (o.&.Hasanetal.1993). or more generally. internal (secular) disk driven evolution. (lxormendsy.&Kennicutt2004):: external mechanisms involve tidal clisruptions or mergers (c.g.Bournaudetal.2007) or nuclear. bombarcment (Melxernan.ctal.2010).," Internal mechanisms involve bars \citep[e.g.][]{b33} or more generally, internal (secular) disk driven evolution \citep{b24}; external mechanisms involve tidal disruptions or mergers \citep[e.g.][]{b41} or nuclear bombardment \citep{b60}."309.. Not all of the material in the ealactic nucleus needs to come from the rest of the ealaxy., Not all of the material in the galactic nucleus needs to come from the rest of the galaxy.310 Material that gains angular momentum close to the accreting supermassive black hole can flow. outwards to be reevelec in the surrounding galactic nucleus (e.g.Ciotti&Alclxernanetal. 2007)..," Material that gains angular momentum close to the accreting supermassive black hole can flow outwards to be recycled in the surrounding galactic nucleus \citep[e.g.][]{b27,b1,b44,b8}."311 Indeed if the feedback. from. the accreting black hole is powerful enough it could disrupt star formation in the galactic nucleus ancl beyond. (Schawinskietal. 2007)., Indeed if the feedback from the accreting black hole is powerful enough it could disrupt star formation in the galactic nucleus and beyond \citep{b1}.312. Outllows from the accreting black hole into the surrounding ealactic nucleus could end up terminating inflows onto the black-hole itself which leads to a picture of ealactic nucleus activity as ποτοσαης (c.g.Youngeretal. 9005).," Outflows from the accreting black hole into the surrounding galactic nucleus could end up terminating inflows onto the black-hole itself, which leads to a picture of galactic nucleus activity as self-regulating \citep[e.g.][]{b38}."313 Isolating the funcamental parameters that. determine the mass aceretion rate onto supermassive black holes is a major observational problem., Isolating the fundamental parameters that determine the mass accretion rate onto supermassive black holes is a major observational problem.314 Many. active galactic nuclei (AGN) are shroudeck by obscuring material (Antonucel 1993).. although the obscuration can be complicated (e.g.Alelxernan&Yaqoob1998:TurnerMiller 2009).," Many active galactic nuclei (AGN) are shrouded by obscuring material \citep{b2}, although the obscuration can be complicated \citep[e.g.][]{b4,b3}."315. ACIN are mostly distant. enough that. broad-band observations include host ealaxy luminosity contributions (e.g. [rom iot dilfuse gas. X-ray binaries ancl ultra-luminous X-rav sources in the A-ray band. alone).," AGN are mostly distant enough that broad-band observations include host galaxy luminosity contributions (e.g. from hot diffuse gas, X-ray binaries and ultra-luminous X-ray sources in the X-ray band alone)."316 One approach to solving this cdillieult: observational problemi is to compare »oacdband buminosities in ACN with fundamental accretion parameters. such as black hole mass. or simple observables such as host galaxy. classification. which may be related to uncdamoental accretion parameters.," One approach to solving this difficult observational problem is to compare broadband luminosities in AGN with fundamental accretion parameters, such as black hole mass, or simple observables such as host galaxy classification, which may be related to fundamental accretion parameters."317 In this work. we investigate the connection between Mack hole mass. host galaxy. classification and the observed Ilt and. X-ray. luminosities of a heterogeneous sample of 276 AGN (mostly from (Melxernanetal. 2009))).," In this work, we investigate the connection between black hole mass, host galaxy classification and the observed IR and X-ray luminosities of a heterogeneous sample of 276 AGN (mostly from \citep{b99}) )."318 In section 2 we investigate the connection between ACGN luminosity. black hole mass and host galaxy. classification.," In section \ref{sec:sample} we investigate the connection between AGN luminosity, black hole mass and host galaxy classification."319 ln section 3. we discuss the AGN luminosity clistribution and in section + we discuss the highly. heterogeneous. non-Sevlert 1. XGN in our sample.," In section \ref{sec:hockey} we discuss the AGN luminosity distribution and in section \ref{sec:group2} we discuss the highly heterogeneous, non-Seyfert 1 AGN in our sample."320 In section r5... we discuss the importance of ringed morphologv in host galaxies and the implications for AGN activity.," In section \ref{sec:rings}, we discuss the importance of ringed morphology in host galaxies and the implications for AGN activity."321 We discuss issues of bias ancl completeness in our sample as well as the reliability of our conclusions in section G and in section 7. we summarize our conclusions.," We discuss issues of bias and completeness in our sample as well as the reliability of our conclusions in section \ref{sec:bias} and in section \ref{sec:conclusions}322 we summarize our conclusions."323 In Melxernanοal.(2009).. for the [first time we compared observed 2-LOkeV X-ray and 19E00pum infra-red Iuminosities in a large. heterogeneous sample of 245 AGN in the literature.," In \citet{b99}, for the first time we compared observed 2-10keV X-ray and $12-100\micron$ infra-red luminosities in a large, heterogeneous sample of 245 AGN in the literature."324 Heterogeneous surveys such as this one include multiple biases and for à discussion of these. see AMelxernanetal.(2009) and Section relsce:bias below.," Heterogeneous surveys such as this one include multiple biases and for a discussion of these, see \citet{b99} and Section \\ref{sec:bias} below."325 In some sources. the relative contribution of an AGN to the Hi and. X-ray luminosity of a LINER. starburst or ULIRG can be debated.," In some sources, the relative contribution of an AGN to the IR and X-ray luminosity of a LINER, starburst or ULIRG can be debated."326 Indeed multiple activity classifications are often given to the same source., Indeed multiple activity classifications are often given to the same source.327 In our sample. since we do not know the relative contribution of the AGNpriori. we do not exclude these objects.," In our sample, since we do not know the relative contribution of the AGN, we do not exclude these objects."328 Furthermore. we avoid model assumptions about specific galactic nuclei or AGN types by. simply using observed luminosities (host galaxy contamination included).," Furthermore, we avoid model assumptions about specific galactic nuclei or AGN types by simply using observed luminosities (host galaxy contamination included)."329 Since AGN classification is complicated. in Melxernanetal.(2009) we simply divided our sample in. two: Croup lL ACN are Seyfert LA AGN (X=0-9) or QSOs.," Since AGN classification is complicated, in \citet{b99} we simply divided our sample in two: Group 1 AGN are Seyfert 1.X AGN (X=0-9) or QSOs."330 Group 2 AGN are evervthing else. (Seyfert 2s. LEINENs. low luminosity. AGN. Starburst(AGN. cross-classified CUN).," Group 2 AGN are everything else (Seyfert 2s, LINERs, low luminosity AGN, Starburst/AGN, cross-classified AGN)."331 Table 1. lists some of the AGN in our sample. with the full sample in a machine-readable table online.," Table \ref{tab:sample} lists some of the AGN in our sample, with the full sample in a machine-readable table online."332 Our key finding in Melxernanetal.(2009) was that. once we removed highly. beamed sources. the in the ratio of observed. Ht to N-rav luminosities in Group 1. AGN is narrow.," Our key finding in \citet{b99} was that, once we removed highly beamed sources, the in the ratio of observed IR to X-ray luminosities in Group 1 AGN is narrow."333 (X. narrow dispersion in physical properties permits the establishment of strong constraints on the physical properties of the ACN. independent. of assumptions about the central engine (c.g. orientation to sightline. clumipy torus. nature of accretion How. extent or patchiness of A-ray corona and. even ACN variability).," A narrow dispersion in physical properties permits the establishment of strong constraints on the physical properties of the AGN, independent of assumptions about the central engine (e.g. orientation to sightline, clumpy torus, nature of accretion flow, extent or patchiness of X-ray corona and even AGN variability)."334 Por this work. we found aclelitional AGN in the literature (Satvapaletal.2005:WrongolelLewis&Ir-al.2010). to add to the sample in Melxernaneta," For this work, we found additional AGN in the literature \citep{b91,b66,b53,b56,b45,b57} to add to the sample in \citet{b99}."335l.(2009)., In Fig.336 In Fig. 1 we plot the mean observed. L2pum [uminosity versus mean observed 2-10keV. luminosity for. the ον in our sample that are not jet-dominated., \ref{fig:hockey} we plot the mean observed $\micron$ luminosity versus mean observed 2-10keV luminosity for the AGN in our sample that are not jet-dominated.337 Black circles correspond. to Group 1 AGN ancl red. crosses correspond o Group 2 AGN., Black circles correspond to Group 1 AGN and red crosses correspond to Group 2 AGN.338 Error bars correspond to the range of observed. luminosities for a given ACN., Error bars correspond to the range of observed luminosities for a given AGN.339 These error. bars (where present) also reveal observer bias in our sample. since jese are the AGN that have been observed multiple times.," These error bars (where present) also reveal observer bias in our sample, since these are the AGN that have been observed multiple times."340 From Fig. l..," From Fig. \ref{fig:hockey},"341 the AGN distribution is generally “hockey-stick’ shaped., the AGN distribution is generally 'hockey-stick' shaped.342 Even including variability. the Group 1 AGN ie in a fairly tight range of [uminositv ratio (90% Lic in re range μον= 1.30]. forming the (black) ‘stick’.," Even including variability, the Group 1 AGN lie in a fairly tight range of luminosity ratio $\%$ lie in the range $R_{IR/X}=[1,30]$ ), forming the (black) 'stick'."343" The Group 2 AGN overlap with the Group 1 AGN but ren [lare out to much larger values of fypix. forming the (red) blade, of the hockey stick."," The Group 2 AGN overlap with the Group 1 AGN but then flare out to much larger values of $R_{IR/X}$, forming the (red) 'blade' of the hockey stick."344 In section 3 below we gaall discuss the significance of the hockey-stick shape of 16 AGN distribution., In section \ref{sec:hockey} below we shall discuss the significance of the hockey-stick shape of the AGN distribution.345 In this section we shall investigate 1e role plaved by. black hole mass and host galaxy. type in 10 observed. LE and. X-ray luminosities of the AGN in our sample., In this section we shall investigate the role played by black hole mass and host galaxy type in the observed IR and X-ray luminosities of the AGN in our sample.346 Since the Group LAGN contain less variation in the vpe and range of activity. we shall investigate these objects inst.," Since the Group 1 AGN contain less variation in the type and range of activity, we shall investigate these objects first."347 ‘To start. we shall investigate the relationship between black," To start, we shall investigate the relationship between black"348]|xeenan et al. (1985)..,Keenan et al. \shortcite{pop_SiII}.349 Although test calculations under the same physical. conditions considered. by the authors appeared to reveal general agreement. it is clillicult to quantify the discrepancies. since they published: their results in graphical form only.," Although test calculations under the same physical conditions considered by the authors appeared to reveal general agreement, it is difficult to quantify the discrepancies, since they published their results in graphical form only."350 We recommend the present calculations to the users. since thev are based on more detailed and accurate atomic cata.," We recommend the present calculations to the users, since they are based on more detailed and accurate atomic data."351" The eround state of the jon is comprised of the ds ""Dyc sextet levels."," The ground state of the $^+$ ion is comprised of the $^6$ 4s $^6\mathrm{D}^e_{\frac{9}{2},\frac{7}{2},\frac{5}{2},\frac{3}{2},\frac{1}{2}}$ sextet levels."352 Comparing to the other atoms/ionspreviously studied. the ion Fe has its fine-structure levels very separated: apart. from cachother and the transition probabilities are considerably higher.," Comparing to the other atoms/ionspreviously studied, the ion $^+$ has its fine-structure levels very separated apart from eachother and the transition probabilities are considerably higher."353 For example. the first. excitatecl level is placed. 384.790 cm|! above the ground level. and. the corresponding transition probability is cles=2.181)5sὃν," For example, the first excitated level is placed 384.790 $^{-1}$ above the ground level, and the corresponding transition probability is $A_{\frac{7}{2}\frac{9}{2}}=2.13\ 10^{-3}\ \mathrm{s}^{-1}$."354 Both factors will contribute to make22 the population ratios of the structure levels of the ion significantly low., Both factors will contribute to make the population ratios of the fine-structure levels of the $^+$ ion significantly low.355" Our model ion includes the four lowest LS terms: 3d""4s σου, 3d' η, 3d""4s !D' and 3d' !P'. making a total of sixteen levels when the fine-structure splitting is accounted for."," Our model ion includes the four lowest LS terms: $^6$ 4s $^6\mathrm{D}^e$, $^7$ $^4\mathrm{F}^e$, $^6$ 4s $^4\mathrm{D}^e$ and $^7$ $^4\mathrm{P}^e$, making a total of sixteen levels when the fine-structure splitting is accounted for."356 The energies were taken from Corliss Sugar (1982) and the transition probabilities from the Iron. Project calculation of Quinet. Le Dourneul Zeippen (1996).|.," The energies were taken from Corliss Sugar \shortcite{E_FeII} and the transition probabilities from the Iron Project calculation of Quinet, Le Dourneuf Zeippen \shortcite{Aij_FeII}357."358 Due to the high separation of the fine-structure levels. the CAIBR will not be an important excitation mechanism.," Due to the high separation of the fine-structure levels, the CMBR will not be an important excitation mechanism."359 For example. at >=5. the excitation rate to the first excited level is just As2=3.510Bol ," For example, at $z=5$, the excitation rate to the first excited level is just $K_{\frac{9}{2}\frac{7}{2}}=3.5\ 10^{-18}\ \mathrm{s}^{-1}$."360The only collisional process for which we could. find detailed excitation. rates calculated in the Literature were collisions by electrons., The only collisional process for which we could find detailed excitation rates calculated in the literature were collisions by electrons.361 Fig., Fig.362" 9. shows the excitation rates by collisions with electrons for the most important. transitions within the D"" ground term.", \ref{figure:qijFeII} shows the excitation rates by collisions with electrons for the most important transitions within the $^6\mathrm{D}^e$ ground term.363 The corresponding \laxwellian-averaged collision strengths were taken from the Iron Project calculation of Zhang Prachan (1995).., The corresponding Maxwellian-averaged collision strengths were taken from the Iron Project calculation of Zhang Pradhan \shortcite{q_e_FeII}.364 Nussbaumoer Storey (1980). estimated the excitation rates by collisions with protons to be less than LO percent of the corresponding excitation rates by collisions. with electrons for temperatures as high as 7=15000 Ix. Llowever. as itis apparent from fig.," Nussbaumer Storey \shortcite{NussStorey} estimated the excitation rates by collisions with protons to be less than 10 percent of the corresponding excitation rates by collisions with electrons for temperatures as high as $T=15000$ K. However, as it is apparent from fig."365 3. and fig. 7.. ," \ref{figure:qijCII} and fig. \ref{figure:qijSiII}, ,"366the excitation rates for collisional processes involving positive tons ancl protons increase rapiclly with temperature. so that one should. be cautious when neeleting collisions bv. protons at extremely high temperatures.," the excitation rates for collisional processes involving positive ions and protons increase rapidly with temperature, so that one should be cautious when negleting collisions by protons at extremely high temperatures."367collected between 2003 and. 2010 caving nme separate observing ruus (see Table 1j).,collected between 2003 and 2010 during nine separate observing runs (see Table \ref{tab:obs}) ).368 All of the data collected with Bolocain has been calibrated using the plaucts (ecnerally Uranus and Neptune). along with sources eiven iu Sandell(1991).," All of the data collected with Bolocam has been calibrated using the planets (generally Uranus and Neptune), along with sources given in \citet{sandell94}."369. The Bolocam flux calibration procedure is described iu detail in Laurentctal.(2005) and Saversetal.(2009)... aud. we briefly describe the details below.," The Bolocam flux calibration procedure is described in detail in \citet{laurent05} and \citet{sayers09}, and we briefly describe the details below."370 Fundamental to our flux calibration technique is the fact that Bolocam coutinnously monitors the operating resistance of the bolometers via the bias carricr amplitude., Fundamental to our flux calibration technique is the fact that Bolocam continuously monitors the operating resistance of the bolometers via the bias carrier amplitude.371 As the transmission of the atmosphere increases the optical load ou the bolomoeters decreases and the operating resistance increases., As the transmission of the atmosphere increases the optical load on the bolometers decreases and the operating resistance increases.372 Additionally. the responsivity Gu uV/Jv) of the bolometers iucreases as the bolometer resistance increases.," Additionally, the responsivity (in nV/Jy) of the bolometers increases as the bolometer resistance increases."373 Cousequeutly. we are able το simultancously account for changes in atimospheric transmission aud detector respousivity bv fittine the flux calibration as a fiction of bias carrier amplitude.," Consequently, we are able to simultaneously account for changes in atmospheric transmission and detector responsivity by fitting the flux calibration as a function of bias carrier amplitude."374 Iu practice. the technique works as follows.," In practice, the technique works as follows."375 For a given observing rui. we generally. observe multiple sources that have coustaut brightuesses," For a given observing run, we generally observe multiple sources that have constant brightnesses."376" We then simultaneously fit the data for all of these sources according to where Vi; is the bolometer response to source i (in nV). Dj; is the brightuess of source ὃν O;; is the solid augle of source { during observation j. is the bolometer resistance during observation j as measuredRy by the bias carrier amplitude. and ay, aud o» describe how the bolometer response changes as a fuuctiou of "," We then simultaneously fit the data for all of these sources according to where $V_i$ is the bolometer response to source $i$ (in nV), $B_i$ is the brightness of source $i$ , $\Omega_{i,j}$ is the solid angle of source $i$ during observation $j$, $R_{j}$ is the bolometer resistance during observation $j$ as measured by the bias carrier amplitude, and $\alpha_1$ and $\alpha_2$ describe how the bolometer response changes as a function of $R_j$."377huplicit in the above formula is the fj.asstuuption that chauges in the overall opacity of the atinosphere are completely accounted for via o4 and o». which iuplies that the atinospheric transnüssion varies dmi a such wav that the shape of the Bolocam baudpass through the atimosphere is coustaut.," Implicit in the above formula is the assumption that changes in the overall opacity of the atmosphere are completely accounted for via $\alpha_1$ and $\alpha_2$, which implies that the atmospheric transmission varies in a such way that the shape of the Bolocam bandpass through the atmosphere is constant."378 However. over the range of conditions where these data were collected (cohunn depths of precipitable water between 0.5 and 3.0 mun). variations in the atmospheric opacity do cause the baudpass to vary (Pardoctal.Haney2001a.b.Dolocama 2005))).," However, over the range of conditions where these data were collected (column depths of precipitable water between 0.5 and 3.0 mm), variations in the atmospheric opacity do cause the Bolocam bandpass to vary slightly \citep{pardo01, pardo01_2, pardo05}) )."379 For a typical Nightlyobserving run. these variations n the atmosphere add an additional uncertainty of zc0.2% to our measured brightucss ratios. which is negligible compared to our nieasurement uncertainties of 15!," For a typical observing run, these bandpass variations in the atmosphere add an additional uncertainty of $\simeq 0.2$ to our measured brightness ratios, which is negligible compared to our measurement uncertainties of $1-5$."380 Note that we have assumed that the angular size of the source is much salle than the angular size of the Bolocaim point-spread function. which is true for all of thesourcest.," Note that we have assumed that the angular size of the source is much smaller than the angular size of the Bolocam point-spread function, which is true for all of the."381. Since the solid angle of both Uranus and Neptune varies with observation epoch. we compute the value of OQ;; separately for cach inteeration of theseplanets usine the James Clerk Maxwell Telescope (ICM). Fluxesprogram.," Since the solid angle of both Uranus and Neptune varies with observation epoch, we compute the value of $\Omega_{i,j}$ separately for each integration of theseplanets using the James Clerk Maxwell Telescope (JCMT) Fluxes."382" For the secondary calibrators. the value of O;,j is asstumed to be constant."," For the secondary calibrators, the value of $\Omega_{i,j}$ is assumed to be constant."383 See Table 2. and Figure 1.., See Table \ref{tab:ratio} and Figure \ref{fig:bolocam_ratios}.384 Seven Bolocana. observing runs contain observatious of both Uranus and Neptune., Seven Bolocam observing runs contain observations of both Uranus and Neptune.385 Iu cach run. we measure the brightuess ratio of Uranus to Neptune with <5% statistical uncertainty.," In each run, we measure the brightness ratio of Uranus to Neptune with $\lesssim 5$ statistical uncertainty."386 If we assiune that the brightucss ratio is constant over the period from 2003 to 2010. then we fud that Ώρα)Bxepune=L027+0.006 with C/DOF=L5," If we assume that the brightness ratio is constant over the period from 2003 to 2010, then we find that $B_{Uranus}/B_{Neptune} = 1.027 \pm 0.006$ with $\chi^2/\textrm{DOF} = 4.5/6$."387 A linear fit versus voar to the data reduces the value of 4?by 0.9. indicating th a linear fit is not required (a F-test shows that νοofrealizatious of constant data would have vielded a F-ratio. inuplug that a constant fit to our data is adequate).," A linear fit versus year to the data reduces the value of $\chi^2$ by 0.9, indicating that a linear fit is not required (a F-test shows that of realizations of constant data would have yielded a larger F-ratio, implying that a constant fit to our data is adequate)."388 Comparing to published results at simular frequencies. ONG find a brightness ratio of 1.016-E0.038 using 150 CIIz data collected between February 1983 aud Mach1981 at the National Radio Ástrouoniv Observatory 12-11 antenna at itt Peak. and G93 find a brightucss ratio of 1.01320.016 using 156 (αν data collected at the JCAIT in λίαν 1990/1992.," Comparing to published results at similar frequencies, O86 find a brightness ratio of $1.016 \pm 0.038$ using 150 GHz data collected between February 1983 and March1984 at the National Radio Astronomy Observatory 12-m antenna at Kitt Peak, and G93 find a brightness ratio of $1.043 \pm 0.016$ using 156 GHz data collected at the JCMT in May 1990/1992."389 The combined 2150 (11data set of OsG. C93. and Bolocamsis well describedbv a coustaut Inightuess ratio of Bryanus/Bxepeun:1.029+ 0.006. with a V2/DOF= 5.1/s.," The combined $\simeq 150$ GHzdata set of O86, G93, and Bolocam is well described by a constant brightness ratio of $B_{Uranus}/B_{Neptune} = 1.029 \pm 0.006$ , with a $\chi^2/\textrm{DOF} = 5.4/8$ ."390 In this case a linear fit versus, In this case a linear fit versus391"where (n;/nu)o is the solar abundance ofelement i (the default solar abundances are given in Table 1)) and Ai,c is the contribution of heavy element i to the radiative cooling rate for solar abundances, which we have tabulated as a function of lognu, log T', and z.","where $(n_i/n_{\rm H})_\odot$ is the solar abundance ofelement $i$ (the default solar abundances are given in Table \ref{tab-abund}) ) and $\Lambda_{i,\odot}$ is the contribution of heavy element $i$ to the radiative cooling rate for solar abundances, which we have tabulated as a function of $\log392n_{\rm H}$, $\log T$ , and $z$."393 Note that we use A to denote the cooling rate per unit volume (ergs!cm 3).," Note that we use $\Lambda$ to denote the cooling rate per unit volume ${\rm394 erg} \,{\rm s}^{-1}\, {\rm cm}^{-3}$ )."395" We can, however, do better than equation (3)) by taking the dependence of the free electron density on He/H, into account (in equation (3)), the electron density is implicitly assumed to be that corresponding to solar abundances - nge/ng= 0.1)."," We can, however, do better than equation \ref{eq:badcoolmethod}) ) by taking the dependence of the free electron density on He/H, into account (in equation \ref{eq:badcoolmethod}) ), the electron density is implicitly assumed to be that corresponding to solar abundances - $n_{{\rm He}}/n_{{\rm H}} = 0.1$ )."396" Since cooling rates due to metals are dominated by collisions between ions and free electrons, A; scales as the product of the free electron and ion densities, Διοςnen;."," Since cooling rates due to metals are dominated by collisions between ions and free electrons, $\Lambda_i$ scales as the product of the free electron and ion densities, $\Lambda_i \propto n_{\rm e} n_i$."397" Hence, where 1003]=(n;/ng)/(ni/mg)e and we used the fact that nH=nm,o (since we tabulate as a function of ng)."," Hence, where $10^{[i/{\rm H}]} \equiv (n_i/n_{\rm H}) / (n_i/n_{\rm H})_\odot$ and we used the fact that $n_{\rm H} = n_{{\rm H},\odot}$ (since we tabulate as a function of $n_{\rm H}$ )."398" While (ne/nH)o is obtained by interpolating the solar abundance table for ne/ny in (ng,2), (Ne/nH) must be obtained by interpolating in ((nHe/nH),T,nH,z)."," While $(n_{\rm e}/n_{\rm399 H})_\odot$ is obtained by interpolating the solar abundance table for $n_{\rm e}/n_{\rm H}$ in $(n_{\rm H},T,z)$, $(n_{\rm e}/n_{\rm400 H})$ must be obtained by interpolating in $((n_{\rm He}/n_{\rm401 H}),n_{\rm H},T,z)$."402 Note that we tabulate the electron density in the absence of metals., Note that we tabulate the electron density in the absence of metals.403 This is a valid approximation given that heavy elements only contribute significantly to the free electron density for Z3Zo., This is a valid approximation given that heavy elements only contribute significantly to the free electron density for $Z \gg Z_{\odot}$.404" In practice we tabulate logA;o/nz over the range log[nu(επι?)]=—8.0, -7.9, ..., 0.0 and log[T(K)]=2.00, 2.02, ..., 9.00."," In practice we tabulate $\log \Lambda_{i,\odot}/n_{\rm H}^2$ over the range $\log[ n_{\rm H}\,(\cm^{-3})] = -8.0$, -7.9, $\ldots$, 0.0 and $\log[T~(\K)] = 2.00$, 2.02, $\ldots$, 9.00."405" In addition, the quantities logAu,ne/ng,ne/ng and the mean particle mass are all tabulated as a function of density and temperature for each of the values nge/ng=0.0787, 0.0830, 0.0876, 0.0922, 0.970, 0.102, 0.107 which correspond to mass fractions Xue/(Xu+Xue)= 0.238, 0.248, 0.258, 0.268, 0.278, 0.288, 0.298."," In addition, the quantities $\log \Lambda_{{\rm H},{\rm He}}/n_{\rm H}^2$,$n_{\rm406 e}/n_{\rm H}$ and the mean particle mass are all tabulated as a function of density and temperature for each of the values $n_{\rm407 He}/n_{\rm H} = 0.0787$, 0.0830, 0.0876, 0.0922, 0.970, 0.102, 0.107 which correspond to mass fractions $X_{\rm He}/(X_{\rm H} + X_{\rm408 He}) = 0.238$ , 0.248, 0.258, 0.268, 0.278, 0.288, 0.298."409" Finally, for each value of the ratio nHe/nH we tabulate the temperature as a function of density and internal energy per unit mass to enable simulation codes that parametrize thermal energy in terms of the latter quantity to use the cooling tables."," Finally, for each value of the ratio $n_{\rm He}/n_{\rm H}$ we tabulate the temperature as a function of density and internal energy per unit mass to enable simulation codes that parametrize thermal energy in terms of the latter quantity to use the cooling tables."410 We have computed these tables for each of the 49 redshifts spanning z=0—9 for which the HMO01 models are defined., We have computed these tables for each of the 49 redshifts spanning $z=0-9$ for which the HM01 models are defined.411 All tables are in HDF5 format and together they result in upwards of 232 MB of storage., All tables are in HDF5 format and together they result in upwards of 232 MB of storage.412" Reducing the resolution in nu and T by a factor of two does reduce the accuracy of interpolated ratessignificantly?,, but reduces the storage requirements to 61 MB."," Reducing the resolution in $n_{\rm H}$ and $T$ by a factor of two does reduce the accuracy of interpolated rates, but reduces the storage requirements to 61 MB."413" We find that for metallicities ZSZo equation (4)) closely matches the true cooling rate (ie., including all elements) with very good if the following 11 elements are included: H, He, C, N, O, Ne, Mg, Si, S, Ca, and Fe."," We find that for metallicities $Z \la Z_\odot$ equation \ref{eq:coolmethod}) ) closely matches the true cooling rate (i.e., including all elements) with very good if the following 11 elements are included: H, He, C, N, O, Ne, Mg, Si, S, Ca, and Fe."414" For redshift z=0 and over the full range of densities and temperatures, the median relative errors in the absolute net cooling rates are0.33%,,1.6%,, and for Z—0.1Zo, Zo, and 10Zo, respectively (we have scaled nge/ng with metallicity)."," For redshift $z=0$ and over the full range of densities and temperatures, the median relative errors in the absolute net cooling rates are, and for $Z = 0.1 Z_{\odot}$, $Z_{\odot}$, and $10415Z_{\odot}$, respectively (we have scaled $n_{{\rm He}}/n_{{\rm H}}$ with metallicity)."416" For higher redshifts the median errors are smaller than for z—0 because Compton cooling off the CMB, which is modelled accurately, becomes increasingly important."," For higher redshifts the median errors are smaller than for $z=0$ because Compton cooling off the CMB, which is modelled accurately, becomes increasingly important."417" Hence, even for metallicities as extreme as 10 times solar, using equation (4)) and including 11 elements gives errors of only a few percent."," Hence, even for metallicities as extreme as 10 times solar, using equation \ref{eq:coolmethod}) ) and including 11 elements gives errors of only a few percent."418" As we shall see below, this is much smaller than the differences between different photo-ionization codes."," As we shall see below, this is much smaller than the differences between different photo-ionization codes."419" Using equation (3)) rather than (4)) gives similar errors for low metallicities, but the median errors are a factor 2-3 higher for Z>1005 Zo."," Using equation \ref{eq:badcoolmethod}) ) rather than \ref{eq:coolmethod}) ) gives similar errors for low metallicities, but the median errors are a factor 2–3 higher for $Z > 10^{0.5}~Z_\odot$ ."420" Excluding temperatures within 0.1 dex ofthe thermal equilibrium solution (where the relative errors in the net cooling rate, which is computed as the absolute difference between heating and cooling, become large because we are subtracting two nearly identical numbers), the maximum errors in the net cooling rates are 32%,, 29%,, and"," Excluding temperatures within 0.1 dex ofthe thermal equilibrium solution (where the relative errors in the net cooling rate, which is computed as the absolute difference between heating and cooling, become large because we are subtracting two nearly identical numbers), the maximum errors in the net cooling rates are , and"421"Let the uncertainties measured on Z,.Q,,.U,, and Vj, for the calibrator(s) be «r.c. and ey. then the corresponding uncertainty on the matrix elements are Due to the non-linearity of the equations involved. it 1s not possible to propagate these errors through the estimate of the cross-terms. to the complete instrumental Mülller matrix.","Let the uncertainties measured on $I_m, Q_m, U_m$ and $V_m$ for the calibrator(s) be $\sigma_I, \sigma_Q, \sigma_U$ and $\sigma_V$, then the corresponding uncertainty on the matrix elements are Due to the non-linearity of the equations involved, it is not possible to propagate these errors through the estimate of the cross-terms, to the complete instrumental Mülller matrix."422" It is anyway possible. by comparing the mathematical definitions of the matrix elements. to use the results to establish an upper limit for the remaining errors. e.g. it is clear from their definition that the error on mi), and ΗΕ must be the same."," It is anyway possible, by comparing the mathematical definitions of the matrix elements, to use the results to establish an upper limit for the remaining errors, e.g. it is clear from their definition that the error on $m_{11}$ and $m_{14}$ must be the same."423" By applying similar qualitative considerations. the complete error matrix can be estimated às The intrinsic Stokes vectorcan be then obtained by inverting T. propagating step by step the errors c, during the inversion process and applying the following Finally. once ὃν is obtained. one or more flux-density calibrators can be used to dermine the K/Jy conversion factor for / and V. and a strongly polarized calibrator can be used to determine the K/Jy conversion factor for Q and U."," By applying similar qualitative considerations, the complete error matrix can be estimated as The intrinsic Stokes vectorcan be then obtained by inverting $\mathbf{T}$ , propagating step by step the errors $\sigma_{nm}$ during the inversion process and applying the following Finally, once $S_s$ is obtained, one or more flux-density calibrators can be used to dermine the K/Jy conversion factor for $I$ and $V$, and a strongly polarized calibrator can be used to determine the K/Jy conversion factor for $Q$ and $U$."424 During the year 2007 several observations were carried out at the 100-m Effelsberg telescope to test the new sub-reflector., During the year 2007 several observations were carried out at the 100-m Effelsberg telescope to test the new sub-reflector.425 Part of this test time has also been used to test the full Stokes polarimetric calibration., Part of this test time has also been used to test the full Stokes polarimetric calibration.426 A selected sample of 43 sources (39 extragalactic sources. 2 planetary nebulae. 2 planets) have been observed nearly monthly at 6 cm.," A selected sample of 43 sources (39 extragalactic sources, 2 planetary nebulae, 2 planets) have been observed nearly monthly at 6 cm."427 Subsequently. some observations at I] em. 3.6 em and 2.8 em were also carried out.," Subsequently, some observations at 11 cm, 3.6 cm and 2.8 cm were also carried out."428 The Stokes parameters measurement listed in Table 4 for the planetary nebula 77027 yielded also the following instrumental terms (averages over time. and standard deviations) These values are in good agreement with the receiver technical specifications.," The Stokes parameters measurement listed in Table \ref{t:pol6} for the planetary nebula 7027 yielded also the following instrumental terms (averages over time, and standard deviations) These values are in good agreement with the receiver technical specifications."429 The measured amplitudes are in good agreement also with EVN measurements., The measured amplitudes are in good agreement also with EVN measurements.430 The definition of D-terms phase in the interferometry processing is quite obscure. so itis unclear whether the results are different or not.," The definition of D-terms phase in the interferometry processing is quite obscure, so it is unclear whether the results are different or not."431 We used our D-term calibration to search for CP in 19 AGNs with improved sensitivity over previous observations at Etfelsberg., We used our D-term calibration to search for CP in 19 AGNs with improved sensitivity over previous observations at Effelsberg.432 Table 5 lists à comparison at 6 em between the raw circular polarization and the values obtained after the calibration. using 77027 as unpolarized calibrator and 2286 as strongly polarized calibrator.," Table \ref{t:CP} lists a comparison at 6 cm between the raw circular polarization and the values obtained after the calibration, using 7027 as unpolarized calibrator and 286 as strongly polarized calibrator."433 The data were observed in. November 2007., The data were observed in November 2007.434 After the D-term calibration. the second planetary nebula. 66572. appears circularly unpolarized as expected.," After the D-term calibration, the second planetary nebula, 6572, appears circularly unpolarized as expected."435 Significant amounts of CP were detected in the two known CP sources 0743-006 and 1519-273 at levels consistent with published levels (0743-006: V.2(—0.514+0.08)%. ?. and V=(-0.46+0.05)%. ?.. both adopting the circular RL frame and for 1519-273: V=(-0.92+0.17)% [?])).," Significant amounts of CP were detected in the two known CP sources 0743-006 and 1519-273 at levels consistent with published levels (0743-006: $V=(-0.51 \pm 0.08) \%$, \citet{Allers} and $V = (-0.46 \pm 0.05) \%$, \citet{Homan}, both adopting the circular RL frame and for 1519-273: $V = (-0.92 \pm 0.17) \%$ \citep{Allers}) )."436 In the Effelsberg measurement of 1519-273. the source appeared unpolarized from the raw values. but the D-terms calibration. revealed a level of CP in good agreement with the values reported in the literature.," In the Effelsberg measurement of 1519-273, the source appeared unpolarized from the raw values, but the D-terms calibration revealed a level of CP in good agreement with the values reported in the literature."437 The Effelsberg measurement of the weakly circularly polarized source 2279 also shows a level of CP close to that published (V=(-0.17+0.01)% |2]))., The Effelsberg measurement of the weakly circularly polarized source 279 also shows a level of CP close to that published $V =(-0.17 \pm 0.01) \%$ \citep{Allers}) ).438 Time variability in CP and changes of sign are very common [?]|.. 1519-273is the most stable CP source known so far.," Time variability in CP and changes of sign are very common \citep{Allers}, , 1519-273is the most stable CP source known so far."439 Table 6 shows a sample of CP values that we observed, Table \ref{t:CPTime} shows a sample of CP values that we observed440exponential-profile magnitude (Stoughtonetal. 2002)) in a motion curve as a measure of an object’s brightness in each wave band at each epoch.,exponential-profile magnitude \citealt{sto2002}) ) in a light-motion curve as a measure of an object's brightness in each wave band at each epoch.441 The PSF magnitude is the optimal measure of the brightness of a point-source object. and hence it is suitable for studying stars and quasars.," The PSF magnitude is the optimal measure of the brightness of a point-source object, and hence it is suitable for studying stars and quasars."442 Photometry of extended objects. such as galaxies. may be performed in a variety of ways. including fitting an exponential profile to the object image.," Photometry of extended objects, such as galaxies, may be performed in a variety of ways, including fitting an exponential profile to the object image."443 The advantage of including the exponential magnitude as opposed to any of the other available profile magnitudes is that the difference between the PSF and exponential magnitudes. referred to as a concentration index. may be used as a continuous object-type classifier (Scrantonetal. 20025). independent of the more restrictive binary SDSS classification.," The advantage of including the exponential magnitude as opposed to any of the other available profile magnitudes is that the difference between the PSF and exponential magnitudes, referred to as a concentration index, may be used as a continuous object-type classifier \citealt{scr2002}) ), independent of the more restrictive binary SDSS classification."444 After processing all Stripe 82 data. the LMCC was trimmed to only those objects that have a mean position in the range a=207 to ia and ὃ=— 17226 to 17226.," After processing all Stripe 82 data, the LMCC was trimmed to only those objects that have a mean position in the range $\alpha = 20.7^{\mbox{\small h}}$ to $^{\mbox{\small h}}$ and $\delta = -$ 26 to 26."445 This was desirable because the temporal coverage is too sparse outside these limits., This was desirable because the temporal coverage is too sparse outside these limits.446 The total, The total447In this section. we quantify the elfect of wet interactions at high redshift on the gas-phase metallicity profiles.,"In this section, we quantify the effect of wet interactions at high redshift on the gas-phase metallicity profiles."448 Similarly to the case of wet interactions in the local Universe. the evolution of metallicity. profiles in the more eas-rich interacting galaxies show a clear Ilattening and the central dilution. of Ο/Η] abundances.," Similarly to the case of wet interactions in the local Universe, the evolution of metallicity profiles in the more gas-rich interacting galaxies show a clear flattening and the central dilution of O/H abundances."449 We quantify the evolution of the metallicity profiles bv. performing linear regressions., We quantify the evolution of the metallicity profiles by performing linear regressions.450 Fig., Fig.451 11. shows the (Ο/Η) and slopes as a function of time (red and. green points. respectively).," \ref{perfiles} shows the $_{C}$ and slopes as a function of time (red and green points, respectively)."452 As expected. we find that the evolution of 411). matches that of the central abundances computed: within Roy (see dotted line of Fig.," As expected, we find that the evolution of $_{C}$ matches that of the central abundances computed within $R_{\rm cen}$ (see dotted line of Fig."453 See)., \ref{gasrich1}c c).454 We can see an increase of the (O/Il)e in around 0.6 dex during the approaching phase while after the first. pericentre. the decrease reflects the impact of the low-metallicity inllows driven by the interactions.," We can see an increase of the $_{C}$ in around 0.6 dex during the approaching phase while after the first pericentre, the decrease reflects the impact of the low-metallicity inflows driven by the interactions."455 These low-metallicity inflows produce a decrease of 0.5 dex in the oxygen central abundance while in less gas-rich counterparts. the decrease is of zz0.2 dex towards the final merging stage (Fig. 6)).," These low-metallicity inflows produce a decrease of $\approx 0.5$ dex in the oxygen central abundance while in less gas-rich counterparts, the decrease is of $\approx4560.2 $ dex towards the final merging stage (Fig. \ref{fit1}) )."457 The evolution of the gradients shows an approximately constant slope until the first pericentre where the profiles eet more negative as a result of the oxween carried into the central region by the carly metal-rich inflows., The evolution of the gradients shows an approximately constant slope until the first pericentre where the profiles get more negative as a result of the oxygen carried into the central region by the early metal-rich inflows.458 However. from the first pericentre there is a continuous mean Lattoning of the metallicity profiles which ects even slightly positive around the second pericentre where again. it starts to be ect steeper toward more negative values às more oxygen is pumped in by SNIE produced during the second. induced starburst (see Fig.," However, from the first pericentre there is a continuous mean flattening of the metallicity profiles which gets even slightly positive around the second pericentre where again, it starts to be get steeper toward more negative values as more oxygen is pumped in by SNII produced during the second tidally-induced starburst (see Fig."459 Sbb)., \ref{gasrich1}b b).460 Several interesting aspects remain to be understood or even acknowledged: in galaxy interactions and their impact. on chemical properties., Several interesting aspects remain to be understood or even acknowledged in galaxy interactions and their impact on chemical properties.461 Numerical simulations are. indeed. the most suitable tool to study them.," Numerical simulations are, indeed, the most suitable tool to study them."462 Dillerent authors with different techniques ancl levels. of NM have mace important NUM (c.g.Perezetal.2006:Rupke2010a:Montuorietal.2010). to this area over the last vears.," Different authors with different techniques and levels of complexity have made important contributions \citep[e.g.][]{perez06,rupke10a,montuori10} to this area over the last years."463 All works agree to dos m central abundance dilution due to low-metallicitv inllows triggered during the interaction., All works agree to show the central abundance dilution due to low-metallicity inflows triggered during the interaction.464 Our simulations allow us to contribute further. to explore the role plaved by the induced SIE and SN feedback in modulating the strength of this metallicity dilution and the evolution of the metallicity gradients., Our simulations allow us to contribute further to explore the role played by the induced SF and SN feedback in modulating the strength of this metallicity dilution and the evolution of the metallicity gradients.465 Particularly. we run Simlll which only follows the dynamics of the gas with fixed metallicity assigned according to an initial abundance prolile.," Particularly, we run SimIII which only follows the dynamics of the gas with fixed metallicity assigned according to an initial abundance profile."466 No new star formation activity is permitted. in Simlll., No new star formation activity is permitted in SimIII.467 As it can be appreciated by comparing the evolution of the 'entral oxveen abundances in Simll and. Simlll in Fig. 12..," As it can be appreciated by comparing the evolution of the central oxygen abundances in SimII and SimIII in Fig. \ref{feedback},"468 neglecting the subsequent star formation ancl chemical enrichment leads to an overestimation of the metallicity cilution (and Hattening of the gradients)., neglecting the subsequent star formation and chemical enrichment leads to an overestimation of the metallicity dilution (and flattening of the gradients).469 One of the ellects of star formation is the generation of new SN IL whieh contributes with new chemical elements and also pumps energv into the ISM., One of the effects of star formation is the generation of new SN II which contributes with new chemical elements and also pumps energy into the ISM.470 Phe strongest. the eas inflows. the strongest the starbursts ancl consequently. the impact of SN feedback. which can heat up ancl blow away significant fractions of the remaining enriched. gas. regulating the subsequent star formation activity and modulating the chemical enrichment.," The strongest the gas inflows, the strongest the starbursts and consequently, the impact of SN feedback which can heat up and blow away significant fractions of the remaining enriched gas, regulating the subsequent star formation activity and modulating the chemical enrichment."471 lo SimlVY we use a lower energy input for SN event and. thus. reducing the impact of energy feedback.," In SimIV we use a lower energy input for SN event and thus, reducing the impact of energy feedback."472 As a consequence. a more intense star formation can develop producing a higher chemical enrichment than in Simll.," As a consequence, a more intense star formation can develop producing a higher chemical enrichment than in SimII."473 From Fig., From Fig.474 12. we can see that he central oxvgen abundance is very similar to that of Simll until the first. pericentre while after that. the mean oxvgen abundance in SimlV is larger since the impact. of he mass-loaced outllows are weaker and are not so cllicient ab transporting material outside the central region and at inhibiting the star formation activity (the ellects on the star ormation rate. a-enhancement and metallicity profiles can oe visualized. comparing results from. Simll ancl SimlV Figs. 3.. 4.," \ref{feedback} we can see that the central oxygen abundance is very similar to that of SimII until the first pericentre while after that, the mean oxygen abundance in SimIV is larger since the impact of the mass-loaded outflows are weaker and are not so efficient at transporting material outside the central region and at inhibiting the star formation activity (the effects on the star formation rate, $\alpha$ -enhancement and metallicity profiles can be visualized comparing results from SimII and SimIV in Figs. \ref{alpha1}, \ref{alpha3},"475 and 6))., and \ref{fit1}) ).476 Hlence. it is important to model the on-going star formation activity in a self-consistent way with energy and chemical SN feedback in order to have a more comprehensive picture of the evolution of the metallicity and eracicnts during galaxy interactions.," Hence, it is important to model the on-going star formation activity in a self-consistent way with energy and chemical SN feedback in order to have a more comprehensive picture of the evolution of the metallicity and gradients during galaxy interactions."477 As à consequence of this complex interplay of various physical processes. we fine that some a priory obvious," As a consequence of this complex interplay of various physical processes, we find that some a priory obvious"478The cosmic star formation rate (SER) is an important observable of our Universe.,The cosmic star formation rate (SFR) is an important observable of our Universe.479 Lt is affected by a variety o£ »hysical processes. many of which are in turn regulated ww the SER. giving rise to so-called feedback loops (for an overview sec. e... Clardi&Ferrara 2005)).," It is affected by a variety of physical processes, many of which are in turn regulated by the SFR, giving rise to so-called feedback loops (for an overview see, e.g., \citealp{Ciardi:2005}) )."480 Photo-ionisation reating due to the absorption of ionising photons from star-orming regions and the injection of kinetic energy. fron supernova (SN) explosions of massive stars provide two such eedback loops., Photo-ionisation heating due to the absorption of ionising photons from star-forming regions and the injection of kinetic energy from supernova (SN) explosions of massive stars provide two such feedback loops.481 Their implications for the assembly. of the irst generation of galaxies have been extensively discussed in studies of the epoch of reionisation (for a review of this epoch see. e... Loch&Barkana 2001).," Their implications for the assembly of the first generation of galaxies have been extensively discussed in studies of the epoch of reionisation (for a review of this epoch see, e.g., \citealp{Loeb:2001}) )."482 Photo-heating associated with reionisation increases the mean temperature of the intergalactie medium (16GM) to ~103Ex (eg. Lui&Gnedin 1997)) and reduces the rate at which hotter gas can cool (Efstathiou1992:Wicrsma.Schave.&Smith 2009)).," Photo-heating associated with reionisation increases the mean temperature of the intergalactic medium (IGM) to $\sim 10^4 \K$ (e.g., \citealp{Hui:1997}) ) and reduces the rate at which hotter gas can cool \citealp{Efstathiou:1992,Wiersma:2008}) )."483 Phe increase in the gas temperature keeps the LGAL smooth anc prevents the assembly. of Iow-mass galaxies. thatis. galaxies with masses corresponding to a virial temperature totls (e.g. Shapiro.Ciroux.&Babul 1994: Cnedin&Lui 1998)).," The increase in the gas temperature keeps the IGM smooth and prevents the assembly of low-mass galaxies, thatis, galaxies with masses corresponding to a virial temperature $\lesssim 10^4 \K$ (e.g., \citealp{Shapiro:1994}; \citealp{Gnedin:1998}) )."484 Moreover.the gas in galaxies that have already collapsed is relatively quickly photo-evaporated (e.g. Shapiro.Hiev.&Raga2004:: Liev.Shapiro.&Raga2005 . strongly decreasing the gas fraction of low-mass halos (e.g... Thoul&Weinberg190601:1999:: Dijkstraetal. 2004: Susa&Umenmura 2006)).," Moreover,the gas in galaxies that have already collapsed is relatively quickly photo-evaporated (e.g., \citealp{Shapiro:2004}; \citealp{Iliev:2005}) ), strongly decreasing the gas fraction of low-mass halos (e.g., \citealp{Thoul:1996}; \citealp{Dijkstra:2004}; ; \citealp{Susa:2006}) )."485 Indeed. the cosmic SER has been predicted: to exhibit a distinct drop around. the redshift of reionisation (Barkana&Loch 2000)).," Indeed, the cosmic SFR has been predicted to exhibit a distinct drop around the redshift of reionisation \citealp{Barkana:2000}) )."486 Photo-ionisation heating is therefore said to provide a negative feedback on SN explosions of massive stars typically inject a few solar masses of eas with velocity of ~10°kms corresponding to a kinetic οποιον of ~107erg.," Photo-ionisation heating is therefore said to provide a negative feedback on SN explosions of massive stars typically inject a few solar masses of gas with velocity of $\sim 10^4\kms$, corresponding to a kinetic energy of $\sim 10^{51} \erg$."487 The ejected material sweeps up and shock-heats the surrounding eas. entraining outllows sullicienthy powerful to. at. least temporarily. substantially reduce. the eas [ractions [or ealaxv-scale dark matter halos (e.g. Yepesetal.1997: Scannapiecoetal. 2006)).," The ejected material sweeps up and shock-heats the surrounding gas, entraining outflows sufficiently powerful to, at least temporarily, substantially reduce the gas fractions for galaxy-scale dark matter halos (e.g., \citealp{Yepes:1997}; \citealp{Scannapieco:2006}) )."488 Since this cads to à suppression of the SER. SN. explosions. like photo-heating from reionisation. xovide a negative [feedback on reionisation.," Since this leads to a suppression of the SFR, SN explosions, like photo-heating from reionisation, provide a negative feedback on reionisation."489 In addition to the depth of the gravitational potential. the ability of SN eedback to reduce the gas fractions generally depends on the geometry of the gas distribution (e.g.. Mac 1999)).," In addition to the depth of the gravitational potential, the ability of SN feedback to reduce the gas fractions generally depends on the geometry of the gas distribution (e.g., \citealp{MacLow:1999}) )."490 Studies of the ellects of photo-heating and SN feedback on the SER. the considered: cach process in isolation have been augmented. by studies. that included. both photo- and SN feedback., Studies of the effects of photo-heating and SN feedback on the SFR that considered each process in isolation have been augmented by studies that included both photo-heating and SN feedback.491" ""ποσο studies include simulations of the formation of the first. stars (e.g... Greifetal. 2007:: Wise&Abel 2008:: Whalenetal. 2008)).of the evolution"," These studies include simulations of the formation of the first stars (e.g., \citealp{Greif:2007}; ; \citealp{Wise:2008}; ; \citealp{Whalen:2008}) ),of the evolution"492This research has been supported by the NASA the grants NAG5-13107 and NNGO5GD36G to the University of Chicago.,This research has been supported by the NASA the grants NAG5-13107 and NNG05GD36G to the University of Chicago.493 Katz&Gunn(1991). Navarro&Benz(1991). Katz(1992).. (Navarro&White1993)... (Steinmetz&Müller1994).. (Navarro&White1994) al.1995).. (Navarroetal.1995;Steinmetz&Müller1994.1995)..," \cite{kg91a}, \cite{nb91a}, \cite{katz92a}, \citep{nw93a}, \citep{sm94a}, \citep{nw94a}494 \citep{nw93a, nw94a, nfw95a}. \citep{nfw95a,sm94a,sm95a}."495 deposited into this gas purely as thermal energy. it will be quickly radiated away. and any impact of feedback from star formation will be lost.," deposited into this gas purely as thermal energy, it will be quickly radiated away, and any impact of feedback from star formation will be lost."496 In addition. if star formation is very efficient in low mass halos at high redshifts. a large number of dense. compact galaxies will form and eventually be incorporated into the inner regions of larger galaxies through hierarchical merging.," In addition, if star formation is very efficient in low mass halos at high redshifts, a large number of dense, compact galaxies will form and eventually be incorporated into the inner regions of larger galaxies through hierarchical merging."497 If these baryonic clumps lose angular momentum to dark halos. the resulting objects will be smaller in extent than if the baryons had been accreted smoothly.," If these baryonic clumps lose angular momentum to dark halos, the resulting objects will be smaller in extent than if the baryons had been accreted smoothly."498 Thus. an early collapse of baryons opens a channel for gas to lose angular momentum. yielding galaxies that are too compact. lack angular momentum. and produce stars overly efficiently compared with observations.," Thus, an early collapse of baryons opens a channel for gas to lose angular momentum, yielding galaxies that are too compact, lack angular momentum, and produce stars overly efficiently compared with observations."499 Subsequent work attempted to alleviate these shortcomings by employing stronger forms of feedback and modifications to the cosmological framework., Subsequent work attempted to alleviate these shortcomings by employing stronger forms of feedback and modifications to the cosmological framework.500 In some cases. the problems noted above were exacerbated.," In some cases, the problems noted above were exacerbated."501 For example. photoheating by a diffuse ultraviolet (UV) background was found to further reduce the angular momentum content of the simulated galaxies (Navarro&Steinmetz1997)..," For example, photoheating by a diffuse ultraviolet (UV) background was found to further reduce the angular momentum content of the simulated galaxies \citep{ns97a}."502 Other efforts included the impact of preheating and gas blow-out from small halos (Sommer-Larsenetal.1999) and the formation of galaxies in a warm dark matter (WDM) cosmology (Sommer-Larsen&Dolgov 2001).., Other efforts included the impact of preheating and gas blow-out from small halos \citep{slgv99a} and the formation of galaxies in a warm dark matter (WDM) cosmology \citep{sld01a}.503 More direct comparisons to observations were made possible by incorporating spectral synthesis techniques into the modeling (Contardoetal.1998) and by using the Tully-Fisher relation to constrain the hierarchical origin of galaxies (Steinmetz&Navarro1999;Steinmetz 2000).," More direct comparisons to observations were made possible by incorporating spectral synthesis techniques into the modeling \citep{csfv98a} and by using the Tully-Fisher relation to constrain the hierarchical origin of galaxies \citep{sn99a, ns00a}."504.. However. the galaxies in these simulations were still too concentrated.," However, the galaxies in these simulations were still too concentrated."505 The most recent studies of disk formation have yielded somewhat more promising results., The most recent studies of disk formation have yielded somewhat more promising results.506 Using a model of self-propagating star formation combined with supernova feedback and a UV background. Sommer-Larsenetal.(2002. produced disk galaxies deficient in angular momentum," Using a model of self-propagating star formation combined with supernova feedback and a UV background, \cite{slgp02a,slgp03a} produced disk galaxies deficient in angular momentum"507on the orbital eccentricity that would be required for consistency with the transit light curve analysis.,on the orbital eccentricity that would be required for consistency with the transit light curve analysis.508 The inimuun eccentricity is obtaimed for the case w=907. correspouding to transits occuring at periccuter.," The minimum eccentricity is obtained for the case $\omega=90\arcdeg$, corresponding to transits occurring at pericenter."509" In that case. ©=0,1238d0.031."," In that case, $e =5100.138 \pm 0.034$."511 Solutions with ο«0.27 can be ound for values of w between 25° aud 1557., Solutions with $e<0.27$ can be found for values of $\omega$ between $25\arcdeg$ and $155\arcdeg$.512 The only objection is that tidal dissipation should jiwe damped out this eccentricity., The only objection is that tidal dissipation should have damped out this eccentricity.513" The characteristic civcularization timescale is 7.~10 Myr assunuus a idal quality factor Q,=100 for the plauct. a rough order-ofmaguitude estimate for a solid planet."," The characteristic circularization timescale is $\tau_c\sim 10$ Myr assuming a tidal quality factor $Q_p=100$ for the planet, a rough order-of-magnitude estimate for a solid planet."514 This is unuch shorter than the estimated stellar age., This is much shorter than the estimated stellar age.515" For an dev body like Neptune with Q,~10!107. the cireularization timescale would be 110 Cr. which is at least not overwhchuinely shorter than the svsteia age."," For an icy body like Neptune with $Q_p \sim 10^4-10^5$, the circularization timescale would be 1–10 Gyr, which is at least not overwhelmingly shorter than the system age."516 The mechanisms and timescales for tidal dissipation are not understood from first principles. aud are poorly constrained by observations.," The mechanisms and timescales for tidal dissipation are not understood from first principles, and are poorly constrained by observations."517 Aud it should be kept in nünd that all of the kuown transiting Neptune-like plancts (CJ 136. Kepler. and HLAT-P-11) all. have sienificautly eccentric orbits.," And it should be kept in mind that all of the known transiting Neptune-like planets (GJ 436, Kepler-4, and HAT-P-11) all have significantly eccentric orbits."518 For these reasous. of all the possibilities we have discussed. we find au eccentric orbit to be the most attractive solution to the radius discrepancy problem.," For these reasons, of all the possibilities we have discussed, we find an eccentric orbit to be the most attractive solution to the radius discrepancy problem."519 We recalculated the transit eplemers utilizing 11 of the 16 midtransit times eiven iu Table 2.., We recalculated the transit ephemeris utilizing 14 of the 16 midtransit times given in Table \ref{tab:epoch}.520 We excluded the two nüdtransit times interred from partial transit heht curve data (epochs 195 and 200). out of concern that the secoud-order airmass correction could not be determined as well iu those cases.," We excluded the two midtransit times inferred from partial transit light curve data (epochs 195 and 200), out of concern that the second-order airmass correction could not be determined as well in those cases."521 We fitted a linear function of transit epoch £. The results were (0)=21510980.7187955+0.000015 (BIDtpp) and P=1-580LOL82+0.00000021 dayspA aud the fit had \?=19.2 with 12 deerees of freedoms.," We fitted a linear function of transit epoch $E$ , The results were $T_c(0) = 2454980.7487955 \pm 0.000045$ $_{\rm TDB}$ ) and $P = 1.58040482 \pm 0.00000024$ days and the fit had $\chi^2 = 19.2$ with 12 degrees of freedom."522 Formally the fit is inconsistent with the linear model with confidence. but we do not consider this to be a significant detection of timing anomalies.," Formally the fit is inconsistent with the linear model with confidence, but we do not consider this to be a significant detection of timing anomalies."523 The right panel of Fig., The right panel of Fig.524 6 shows the residuals to the Huear fit., \ref{fig:omc} shows the residuals to the linear fit.525 This plot also shows four data points frou Cliubonucau et ((2009). which ave consistent with the linear model.," This plot also shows four data points from Charbonneau et (2009), which are consistent with the linear model."526 Since is no clear evidence for transit timing variatious (TTVs). we mav use the timing data to place upper luits ou the mass of a lbypothetical second planet that would perturh the orbit of the trausitine planet.," Since is no clear evidence for transit timing variations (TTVs), we may use the timing data to place upper limits on the mass of a hypothetical second planet that would perturb the orbit of the transiting planet."527 To do so. we used au mipleimieutation of the algorithin advocated by Steffen Agol (2005).," To do so, we used an implementation of the algorithm advocated by Steffen Agol (2005)."528 We explore the parameter space of the lwpothetical perturber’s mass and orbital period and phase., We explored the parameter space of the hypothetical perturber's mass and orbital period and phase.529 We assunued the orbits of the perturber aud CJ1211 were circular ane coplanar., We assumed the orbits of the perturber and GJ1214 were circular and coplanar.530 Regions in parameter space vielding dviauuica instability. deterimüned following the prescription by Darues Creeubere (2006). were not sampled.," Regions in parameter space yielding dynamical instability, determined following the prescription by Barnes Greenberg (2006), were not sampled."531 For cach orbital period ranging from 0.38 davs and samplne al orbital phases. the mass of the perturber was increascc until the computed trausit times would fit our data A\?=9 worse than a linear ephemeris: this mass is interpreted as a coufidence wpper-limit.," For each orbital period ranging from 0.3–8 days and sampling all orbital phases, the mass of the perturber was increased until the computed transit times would fit our data $\Delta \chi^2 = 9$ worse than a linear ephemeris; this mass is interpreted as a confidence upper-limit."532 Fig., Fig.533 8 shows the coustraints ou the perturber mass as a function of period ratio. as determined from this analysis.," \ref{fig:masslimits} shows the constraints on the perturber mass as a function of period ratio, as determined from this analysis."534 For reference. on the rght-haud axis we have included the masses of GJ 1211b (6.6 Αι) the Moon (0.01. AZ). and Eris (0.003 374).," For reference, on the right-hand axis we have included the masses of GJ 1214b (6.6 $M_\oplus$ ), the Moon (0.01 $M_\earth$ ), and Eris (0.003 $M_\earth$ )."535 In this plot we have also indicated the zones of dvuanical instability. aud of potential habitability (equilibrium tempcrature between 273373 Is. for an assumed albedo of zero}.," In this plot we have also indicated the zones of dynamical instability, and of potential habitability (equilibrium temperature between 273–373 K, for an assumed albedo of zero)."536 We have also plotted a line corresponding to an RV amplitude of 2unrs . probably the best achievable detection limi based only on RV observations for the near future.," We have also plotted a line corresponding to an RV amplitude of 2 m $^{-1}$, probably the best achievable detection limit based only on RV observations for the near future."537 The imass constraints on the perturber are more restrictive near the mean-motion resonances aud nios restrictive at the low-order resonances. particularly for the iuterior and exterior 2:1 resonances.," The mass constraints on the perturber are more restrictive near the mean-motion resonances and most restrictive at the low-order resonances, particularly for the interior and exterior 2:1 resonances."538 For example. a perturber at the interior 2:1 resonance having mass near that of Eris would have iuduced detectable TTVs with the present data.," For example, a perturber at the interior 2:1 resonance having mass near that of Eris would have induced detectable TTVs with the present data."539 One of our goals in this study was to improve on the estimates of the basic parameters of CJ 121th., One of our goals in this study was to improve on the estimates of the basic parameters of GJ 1214b.540 Yet despite having undertaken many ligh-precisiou observations of trausits. we lave not siguificautlv inproved on the estimate of the planetary radius.," Yet despite having undertaken many high-precision observations of transits, we have not significantly improved on the estimate of the planetary radius."541 Iu our analysis has led us to conclude that the radius 1s even more uncertain than had Όσοι recognized previously., In our analysis has led us to conclude that the radius is even more uncertain than had been recognized previously.542 This is for two reasons., This is for two reasons.543 First. the clear evidence for starspots iu our most precise light curves has caused us to consider the possible effects of stellar activity on he analvsis of transit plotometiyv.," First, the clear evidence for starspots in our most precise light curves has caused us to consider the possible effects of stellar activity on the analysis of transit photometry."544 Second. aud more imuportantlv. we have found a siguif&cant disaerecmenut vetween two dgnethods of cstimating the stellar and dauetarv dimensions. with no good reason why cither oue should be disregarded or considered less trustworthy.," Second, and more importantly, we have found a significant disagreement between two methods of estimating the stellar and planetary dimensions, with no good reason why either one should be disregarded or considered less trustworthy."545 Both of these complications were known prior to this work2009). but we have sought them into focus.," Both of these complications were known prior to this work, but we have brought them into focus."546 The problemi of star spots can be nütigated by serving iu louger-waveleusth bandpasses., The problem of star spots can be mitigated by observing in longer-wavelength bandpasses.547 This is ecause the flux contrast between two blackbodies of different teniperatures is a decreasing function of wavelength., This is because the flux contrast between two blackbodies of different temperatures is a decreasing function of wavelength.548assune the particular starspots that produced anomalies in our data are approxinatelv the same size as the planet. then they are 2:150 Ix cooler than the stellar photosphere (see 3.2. for details).," the particular starspots that produced anomalies in our data are approximately the same size as the planet, then they are $\approx$ 150 K cooler than the stellar photosphere (see \ref{sec:spotcross} for details)."549 This corresponds to a surface-briehtuess ratio of about 0.67 between the spots aud the surroundiugplotosphere.. at an observing wavelength of 0.6 gan. At 3.5 yon. the surface-brightuess ratio would be about 0.91. represeutiug a sinaller contrast aud corresponudiueglv «λαο starspotdnuduced effects.," This corresponds to a surface-brightness ratio of about 0.67 between the spots and the surrounding, at an observing wavelength of 0.6 $\mu$ m. At 3.5 $\mu$ m, the surface-brightness ratio would be about 0.91, representing a smaller contrast and correspondingly smaller starspot-induced effects."550 Theproblem of the stellar radius will be more difficult to solve. and there is mich at stake.," Theproblem of the stellar radius will be more difficult to solve, and there is much at stake."551 The mean planetary deusity could be L.89+0.33 ¢ 2 or 3.03280.50 e cur7. depending ou which route is taken to estimate the stellar radius.," The mean planetary density could be $1.89 \pm 0.33$ g $^{-3}$ or $3.03 \pm 0.50$ g $^{-3}$, depending on which route is taken to estimate the stellar radius."552 The lower density would imply that the planet must have a dense gaseous atinosphere. for which there are many intriguing possible origins auk colpositious (Rogers Seager 2010. Miller-Ricci Fortuev 2010).," The lower density would imply that the planet must have a dense gaseous atmosphere, for which there are many intriguing possible origins and compositions (Rogers Seager 2010, Miller-Ricci Fortney 2010)."553 In contrast. the higher density couk be cousistent with a solid planet with a very thin (or nonexisteut) atmosphere.," In contrast, the higher density could be consistent with a solid planet with a very thin (or nonexistent) atmosphere."554 We have discussed severa possible resolutions of this discrepancy. aud argued that the mostattractive possibility is that the planet has au eccentric orbit. ο5ο 0.11.," We have discussed several possible resolutions of this discrepancy, and argued that the mostattractive possibility is that the planet has an eccentric orbit, $e \approx 0.14$ ."555 This lbypothesis can be testec, This hypothesis can be tested556lines as references.,lines as references.557 The full data set cousists of three temporal series: cach of them lasting about oue hour., The full data set consists of three temporal series; each of them lasting about one hour.558 Three scan steps with 5 step width were taken for the two first series. while in he last series only two spatial positions were used.," Three scan steps with $0''5$ step width were taken for the two first series, while in the last series only two spatial positions were used."559 The cadence was differeut for all series., The cadence was different for all series.560 Table 1. shows the ine step between two spectra taken at the same spatial »oxitiou. the time when the observation were obtained and the uunber of repetitious of cach series.," Table \ref{tb:observation} shows the time step between two spectra taken at the same spatial position, the time when the observation were obtained and the number of repetitions of each series."561 Due to the differential refraction in the earth atmosphere (ee...Filippeuko1982).. the spectra of POLIS aud TIP-II are not fully co-spatial.," Due to the differential refraction in the earth atmosphere \citep[e.g.,][]{Filippenko1982}, the spectra of POLIS and TIP-II are not fully co-spatial."562 The spatia displacement of the two wavelengths (3968À.. 10830 Aj) perpendicular to the slit depends on the date aux iue of the observations. the slit orientation. aud the ocation of the first coclostat mirror (seeAppendixAofDecketal. 2008).," The spatial displacement of the two wavelengths (3968, 10830 ) perpendicular to the slit depends on the date and time of the observations, the slit orientation, and the location of the first coelostat mirror \citep[see Appendix A of][]{Beck+etal2008}."563. Ou the first day of the observation canrpaien. we took a set of large-area scans at ciffereu lunes for an accurate deteruunation of the displacemoent.," On the first day of the observation campaign, we took a set of large-area scans at different times for an accurate determination of the displacement."564 The solid line iun Fig., The solid line in Fig.565 25— shows the theoretically xedieted spatial displacement perpendicular to the xli due to differential refraction. while the asterisks are he measured displacements: the match between both is remarkable.," \ref{fig:refraction} shows the theoretically predicted spatial displacement perpendicular to the slit due to differential refraction, while the asterisks are the measured displacements; the match between both is remarkable."566 To enarautee an overlap between the observations in the two waveleneths. we thus positionc: he scan murror inside of POLIS at the beeinnine of cach observation such that it compensated the spatia displacement for about the middle of the observation.," To guarantee an overlap between the observations in the two wavelengths, we thus positioned the scan mirror inside of POLIS at the beginning of each observation such that it compensated the spatial displacement for about the middle of the observation."567 Moreover. small repeated scans of 2-3 slit spatia yositions. separated by (075. were taken in order to sample a wider region of the Sun and prevent possible errors between the theoretical ciffercutial refraction aux he actual one.," Moreover, small repeated scans of 2-3 slit spatial positions, separated by $0''5$, were taken in order to sample a wider region of the Sun and prevent possible errors between the theoretical differential refraction and the actual one."568 Figure d. shows anu intensity map from a waveleneth in the infrared coutimmun., Figure \ref{fig:intensity} shows an intensity map from a wavelength in the infrared continuum.569 The regious of quiet Sun. sclmuubra. aud umbra of the suuspot are well defined. he vertical lines indicate the boundaries between these areas.," The regions of quiet Sun, penumbra, and umbra of the sunspot are well defined, the vertical lines indicate the boundaries between these areas."570 The temporal evolution of the Stokes 7 aud Stokes V. spectra for the TIP data aud the iuteusity around the ccore in the POLIS data are plotted in Fig., The temporal evolution of the Stokes $I$ and Stokes $V$ spectra for the TIP data and the intensity around the core in the POLIS data are plotted in Fig.571 2 at a fixed »oxition inside the uubra., \ref{fig:spectra} at a fixed position inside the umbra.572 The Stokes £ and W profiles youn TIP contain the liue at AA =0 ((the rest waveleneth of the silicon line was determined roni the quiet Sun region and was sot as the origin) aud he line at AX =3.25Α., The Stokes $I$ and $V$ profiles from TIP contain the line at $\Delta\lambda=$ 0 (the rest wavelength of the silicon line was determined from the quiet Sun region and was set as the origin) and the line at $\Delta\lambda=$ 3.25.573. The helinm line profile shows xeriodie shifts with huge displacements to the blue aud he red., The helium line profile shows periodic shifts with large displacements to the blue and the red.574 The core of the liueσα shows a strong emission peas inside the umbra., The core of the line shows a strong emission peak inside the umbra.575 The Doppler shift of this cussion peak develop a saw-tooth ottern. similar to the liueσα (seealsoRouppevanderVoortetal.2003).," The Doppler shift of this emission peak develop a saw-tooth pattern, similar to the line \citep[see also][]{Rouppe+etal2003}."576. Iu this paper. we focus ou the line-of-sight (LOS) velocities.," In this paper, we focus on the line-of-sight (LOS) velocities."577 For all the spectral lines besidesIL. Doppler velocities were inferred by measuring the xositiou of the iuteusity nininmna.," For all the spectral lines besides, Doppler velocities were inferred by measuring the position of the intensity minimum."578 The waveleneths close o the core of the line were fitted with a second. order xolvnonmial., The wavelengths close to the core of the line were fitted with a second order polynomial.579" The location of the wim, of the parabola was taken as the line-core position.", The location of the minimum of the parabola was taken as the line-core position.580 This procedure was formed to obtain the Doppler shifts ofSir.Wel. aud he lines at 3965.15. 3966.07. 3966.63. 3967.12 and 3969.26A.," This procedure was performed to obtain the Doppler shifts of, and the lines at 3965.45, 3966.07, 3966.63, 3967.42 and 3969.26."581. Inu the case of the TIP data. the Doppler shift of he Stokes V. zero crossing. where the polarization signal intersects the zero level. was derived as well.," In the case of the TIP data, the Doppler shift of the Stokes $V$ zero crossing, where the polarization signal intersects the zero level, was derived as well."582 The Doppler shifts from the iutensitv aud Stokes V profiles are very sinular duc to the huge maguctic πιο factor iu the sunspot mubra., The Doppler shifts from the intensity and Stokes $V$ profiles are very similar due to the large magnetic filling factor in the sunspot umbra.583 The behavior of the ccore is different., The behavior of the core is different.584 It exhibits a prominent peak at the ceuter of the line in highly maeuetized regions (top line of Fie. D).," It exhibits a prominent peak at the center of the line in highly magnetized regions (top line of Fig. \ref{fig:profile_Ca}) ),"585 while in a field-tree atinosphere the ceuter of the ine has a minima between two lobes at both sides with heir corresponding maxima (bottom line of Fie. 1)) (seealso.e.g..Liu&Sinith 1972).," while in a field-free atmosphere the center of the line has a minimum between two lobes at both sides with their corresponding maxima (bottom line of Fig. \ref{fig:profile_Ca}) ) \citep[see also,586e.g.,][]{Liu+Smith1972}."587. In the mubra. the Doppler shift was retrieved from the spectral displacement of the uaxiuun of the core emission.," In the umbra, the Doppler shift was retrieved from the spectral displacement of the maximum of the core emission."588 Iu the low magnetized. reeion it was obtaiued from the shift of the central nuininmuu.," In the low magnetized, region it was obtained from the shift of the central minimum."589 AM iu all. we have obtained maps of the LOS velocity at cach spatial poiut covered by the slit at the corluation heights of the eight spectral lines. except forTet. whose line depth in the nouauagnetized regious 1s oo slnall to determine its location.," All in all, we have obtained maps of the LOS velocity at each spatial point covered by the slit at the formation heights of the eight spectral lines, except for, whose line depth in the non-magnetized regions is too small to determine its location."590 We have selected. the scan steps which eive. tle best aliguiment of the data from both imstimments to obtain a better correction of the differcutial refraction., We have selected the scan steps which give the best alignment of the data from both instruments to obtain a better correction of the differential refraction.591 The use of cifferent steps introduce a systematic delay between the oscillatory signals frou POLIS and TIP-IL since the same spatial location is observed with a time lag.," The use of different steps introduce a systematic delay between the oscillatory signals from POLIS and TIP-II, since the same spatial location is observed with a time lag."592 However. in the case of the data from series 3. the theoretical correction of the differential refraction worked perfectly and the optimal aliguimieut was found using the simultaneous scan steps.," However, in the case of the data from series 3, the theoretical correction of the differential refraction worked perfectly and the optimal alignment was found using the simultaneous scan steps."593 This data set has been chosen to calculate the phase difference spectra from Section 3.3.., This data set has been chosen to calculate the phase difference spectra from Section \ref{sect:phase_spectras}.594 Au additional finer aliguiment along the slit between TIP and POLIS was doue by a cross-correlation of the velocity naps of two spectral lines formed at similar heights. sing the line pair and or the chromosphere. aud and À 3969.26 for the photosphere.," An additional finer alignment along the slit between TIP and POLIS was done by a cross-correlation of the velocity maps of two spectral lines formed at similar heights, using the line pair and for the chromosphere, and and $\lambda$ 3969.26 for the photosphere."595 Finally. we resampled all velocity naps with the sampling of the POLIS data.4&6... 0729 per pixel.," Finally, we resampled all velocity maps with the sampling of the POLIS data, $0''29$ per pixel."596" Figue 5"" shows the temporal evolution of the LOS velocities iu the sunspot region obtained from the Doppler shift of several spectral lines. sorted bv formation height."," Figure \ref{fig:velocity_maps} shows the temporal evolution of the LOS velocities in the sunspot region obtained from the Doppler shift of several spectral lines, sorted by formation height."597 Negative velocities (appearing as black shaded regions) indicate/ upflows. where matter is approaching the observer. while white regions are downflows.," Negative velocities (appearing as black shaded regions) indicate upflows, where matter is approaching the observer, while white regions are downflows."598 Fieures 5((a-d) reveal a simular pattern since, Figures \ref{fig:velocity_maps}( (a-d) reveal a similar pattern since599as a rough estimate of errors at 5 GHz.,as a rough estimate of errors at 5 GHz.600" Since this error is antenna based, our observations covering a parallactic angle range of rreduces the effect by about30%."," Since this error is antenna based, our observations covering a parallactic angle range of reduces the effect by about."601". More importantly, the diffuse polarized emission discussed in this work has no total intensity counterpart, so errors in Stokes Q and U scale with Stokes Q and U, instead of Stokes I (Saultetal.1996)."," More importantly, the diffuse polarized emission discussed in this work has no total intensity counterpart, so errors in Stokes Q and U scale with Stokes Q and U, instead of Stokes I \citep{s96}."602". Furthermore, measurements of RM are not biased by the leakage, but the change in leakage with frequency, which tends to be smaller."," Furthermore, measurements of RM are not biased by the leakage, but the change in leakage with frequency, which tends to be smaller."603" Considering all these effects, we expect position-dependent leakage errors to be less of Stokes Q and U, less than the typical flux calibration errors and unlikely to affect the results presented here."," Considering all these effects, we expect position-dependent leakage errors to be less of Stokes Q and U, less than the typical flux calibration errors and unlikely to affect the results presented here."604 Section 9.2 compares our results to previous GC polarimetry observations and generally confirms this assumption., Section \ref{poln_comparison} compares our results to previous GC polarimetry observations and generally confirms this assumption.605" Finally, it is important to consider the fact that interferometric observations are not sensitive to emission on large angular scales (Haverkornetal.2004;Schnitzeleretal. 2009)."," Finally, it is important to consider the fact that interferometric observations are not sensitive to emission on large angular scales \citep{h04,s09}."606. Missing Q and U flux can create spurious polarization and bias RM values., Missing Q and U flux can create spurious polarization and bias RM values.607 Haverkornetal. show that a wide distribution of RM randomizes (2004)any uniform polarized background and reduces the missing flux., \citet{h04} show that a wide distribution of RM randomizes any uniform polarized background and reduces the missing flux.608" The RM distribution observed here (described in detail in refpadianalysis)) has a width of about 500 rad m? on size scales used in this study (>100”)), which limits the missing flux to less than0."," The RM distribution observed here (described in detail in \\ref{padianalysis}) ) has a width of about 500 rad $^{-2}$ on size scales used in this study $>$ ), which limits the missing flux to less than."609"2%.. As an alternative derivation of missing flux, Schnitzeleretal.(2009) show that a gradient in RM can shift the spatial scale at which polarized emission is visible."," As an alternative derivation of missing flux, \citet{s09} show that a gradient in RM can shift the spatial scale at which polarized emission is visible."610" For the RM gradient seen here (z5 rad m? that technique predicts a shift in spatial scales from arcsec~!),zero to about 1200 A, larger than our shortest baseline."," For the RM gradient seen here $\approx5$ rad $^{-2}$ $^{-1}$ ), that technique predicts a shift in spatial scales from zero to about 1200 $\lambda$, larger than our shortest baseline."611 Both techniques indicate that an insignificant amount of polarized flux is missed by the present observations., Both techniques indicate that an insignificant amount of polarized flux is missed by the present observations.612" To study the RM across this field, mosaics of the polarization angle were differenced between the two bands."," To study the RM across this field, mosaics of the polarization angle were differenced between the two bands."613 The polarization angle difference image (hereafter iimage) was created by differencing the polarization angle images (04s35GHz— 94.835GHz) and remapping each value of tto the range tto90?., The polarization angle difference image (hereafter image) was created by differencing the polarization angle images $\theta_{\rm{4.885 GHz}}-\theta_{\rm{4.835 GHz}}$ ) and remapping each value of to the range to.614. Figure 3 shows the iimage and its error., Figure \ref{poln_padi} shows the image and its error.615" Observationally, the rotation measure is defined as RM=A0/A(X?)."," Observationally, the rotation measure is defined as $ = \Delta\theta/\Delta(\lambda^2)$."616" Assuming this M law, a position angle difference of ccorresponds to a rotation measure of -220 rad m~?."," Assuming this $\lambda^2$ law, a position angle difference of corresponds to a rotation measure of –220 rad $^{-2}$."617" More generally, the observed polarization is the sum of polarized emission emitted with a range of RM (Burn1966;Brentjens&deBruyn 2005)."," More generally, the observed polarization is the sum of polarized emission emitted with a range of RM \citep{b66,br05}."618. Such complex sources can have non-quadratic changes in the polarization angle that can confuse a simple analysis., Such complex sources can have non-quadratic changes in the polarization angle that can confuse a simple analysis.619" In these situations, the pertinent physical quantity is the Faraday depth"": where ne is in cm?, H is in G, and di is in pe."," In these situations, the pertinent physical quantity is the “Faraday depth”: where $n_e$ is in $^{-3}$, $\vec{B}$ is in G, and $d\vec{l}$ is in pc."620" For simple physical distributions of n, aand B, $ iis equal to RM."," For simple physical distributions of $n_e$ and $\vec{B}$, $\phi$ is equal to RM."621" However, robustly tying the RM to physical conditions in complex cases requires measurements at many wavelengths (Brentjens&deBruyn2005)."," However, robustly tying the RM to physical conditions in complex cases requires measurements at many wavelengths \citep{br05}."622". Since we only have two wavelengths to study the polarization in this region, we instead use this formalism to define the limits of deriving physical conditions from the observed RM."," Since we only have two wavelengths to study the polarization in this region, we instead use this formalism to define the limits of deriving physical conditions from the observed RM."623" First, the formalism of Brentjens&deBruyn shows that the spacing of the bands in wavelength(2005) determines the “RM resolution"" and possible na ambiguities."," First, the formalism of \citet{br05} shows that the spacing of the bands in wavelength determines the “RM resolution” and possible $n\pi$ ambiguities."624" For thetwo bands used here, the RM resolution is 4x104 rrad m~? and any aliasing occurs at RM=n*4x104 rad m-?, for an integer m."," For thetwo bands used here, the RM resolution is $4\times10^4$ rad $^{-2}$ and any aliasing occurs at $=n * 4\times10^4$ rad $^{-2}$, for an integer $n$."625" The RM expected in the GC region covered by this survey is typically «2000 rrad πι. (Yusef-Zadehetal.1984;Tsuboiet1986;Roy 2005), so there is little chance of an na ambiguity."," The RM expected in the GC region covered by this survey is typically $<2000$ rad $^{-2}$ \citep{y84,t86,r05}, so there is little chance of an $n\pi$ ambiguity."626" Second, the bandwidth determines the amount of Faraday rotation within a band, which limits the maximum Faraday depth detectable {οφ«2x10* rrad τα."," Second, the bandwidth determines the amount of Faraday rotation within a band, which limits the maximum Faraday depth detectable to $\phi<2\times10^4$ rad $^{-2}$ ."627" Finally, a source that emits over a range of Faraday depths, known as *Faraday thick"", can be internally depolarized."," Finally, a source that emits over a range of Faraday depths, known as “Faraday thick”, can be internally depolarized."628 The maximum, The maximum629As noted in Sect. 2.3..,"As noted in Sect. \ref{sec:transitionrates},"630 it can be important to include the highest levels of the atom in the calculations., it can be important to include the highest levels of the atom in the calculations.631 It is not necessary to include each individual level however. and it is possible to use superlevels that represent groups of closely spaced levels (2).," It is not necessary to include each individual level however, and it is possible to use superlevels that represent groups of closely spaced levels \citep{Korn2008}."632 To test the effect of these upper levels. we took the approach of giving the top 0.5 eV of levels in our atomic model an Sy = 2 whilst the rest of the levels had Sy = |.," To test the effect of these upper levels, we took the approach of giving the top 0.5 eV of levels in our atomic model an $\rm S_{H}$ = 2 whilst the rest of the levels had $\rm S_{H}$ = 1."633 We have done this for three situations: A) increasing Sy for just the bound transitions rates. B) increasing Sy for Just the bound-free rates and C) increasing Sy for both the bound-bound and bound-free.," We have done this for three situations; A) increasing $\rm S_{H}$ for just the bound-bound transitions rates, B) increasing $\rm S_{H}$ for just the bound-free rates and C) increasing $\rm S_{H}$ for both the bound-bound and bound-free."634 We discuss here only the case of the bound-free rates as it is only these rates that have an effect. edging the populations towards LTE values.," We discuss here only the case of the bound-free rates as it is only these rates that have an effect, edging the populations towards LTE values."635 Changing the bound-free rates not only affects the higher levels but translates through all lower ones., Changing the bound-free rates not only affects the higher levels but translates through all lower ones.636 In fact it is the lower half of the atomic model that is affected by a greater amount; further investigation into reasons for this effect are discussed in Sect. 6.1.., In fact it is the lower half of the atomic model that is affected by a greater amount; further investigation into reasons for this effect are discussed in Sect. \ref{sec:TheTRmEffScale}.637 The result can be seer in Fig., The result can be seen in Fig.638 6 where we plot a level with y = 0.96 eV and one of the higher levels. y = 3.30 eV. from our atomie model.," \ref{fig:ULeffects} where we plot a level with $\chi$ = 0.96 eV and one of the higher levels, $\chi$ = 3.30 eV, from our atomic model."639 Fig., Fig.640 7 shows the abundance correction against y for the increased Su value of the upper levels and for a pure Sy = | situation., \ref{fig:chiAULeffect} shows the abundance correction against $\chi$ for the increased $\rm S_{H}$ value of the upper levels and for a pure $\rm S_{H}$ = 1 situation.641" Comparing the differences in abundance correction between Sy = 1. and Sy = | with Sy = 2 on the upper levels we see a meat difference (AA(Fe)s,4» — AACFe)s, 1) of 20.031 dex for y = O0 - 2 eV and —0.028 dex for y> 2 eV. for the star HD140283."," Comparing the differences in abundance correction between $\rm S_{H}$ = 1, and $\rm S_{H}$ = 1 with $\rm S_{H}$ = 2 on the upper levels we see a mean difference $\Delta A(\rm Fe)_{S_H=1+2}$ – $\Delta A(\rm Fe)_{S_{H}=1}$ ) of $-0.031$ dex for $\chi$ = 0 - 2 eV and $-0.028$ dex for $\chi >$ 2 eV, for the star HD140283."642 These effects equate to a 5 K increase in Ty compared to Sy , These effects equate to a 5 K increase in $T_{\rm eff}$ compared to $\rm S_{H}$ 643distributions are found using the mentioned type of transport equation.,distributions are found using the mentioned type of transport equation.644 This allows to account for the synchrotron cooling suffered before the decay of this secondary. transient particles.," This allows to account for the synchrotron cooling suffered before the decay of this secondary, transient particles."645 We have found that the radiative output obtained can account for much of the observational data for the two radiogalaxies M87 and AA. As seen in Figs., We have found that the radiative output obtained can account for much of the observational data for the two radiogalaxies M87 and A. As seen in Figs.646 5. and 9.. the model allows for the possibility of explaining the VHE emission by means of pp interactions.," \ref{SED_cena} and \ref{sed-M87}, the model allows for the possibility of explaining the VHE emission by means of $pp$ interactions."647 The hard X-ray data corresponds to electron synchrotron radiation whereas the y emission is well reproduced by proton synchrotron and IC emission., The hard X-ray data corresponds to electron synchrotron radiation whereas the $\gamma$ emission is well reproduced by proton synchrotron and IC emission.648?. A previous one-zone lepto-hadronie model for AA was proposed by just before HESS and Fermi/LAT data was available., A previous one-zone lepto-hadronic model for A was proposed by just before HESS and Fermi/LAT data was available.649 In. the present. work. we have included the effects of absorption due to phototonization interactions in. the surroundingmedium.," In the present work, we have included the effects of absorption due to photoionization interactions in the surrounding."650 This causes a drastic modulation in the electron synchrotron spectrum. especially for AA. which is responsible for the whole emission in the broadband range ~10°— 10%eV. In the case of M87. this type of absorption has a minor impact. since the column density is much less (Ny=2κ0 σπα”. ?).," This causes a drastic modulation in the electron synchrotron spectrum, especially for A, which is responsible for the whole emission in the broadband range $\sim 10^{-5}-10^{7}$ eV. In the case of M87, this type of absorption has a minor impact, since the column density is much less $N_H=2 \times 10^{20}{\rm cm}^{-2}$ , )."651 The internal absorption of gamma-rays Is also taken into account. being important only within the injection zone. where the synchrotron emission of primary electrons provide an important absorbing target.," The internal absorption of gamma-rays is also taken into account, being important only within the injection zone, where the synchrotron emission of primary electrons provide an important absorbing target."652 It is important to note that the same model can be used to describe different types of jet., It is important to note that the same model can be used to describe different types of jet.653 In terms of the broadband photon emission. M87 data shows a similar luminosity level for high and the low energy ranges.," In terms of the broadband photon emission, M87 data shows a similar luminosity level for high and the low energy ranges."654 Since the VHE emission ts basically determined by pp interactions. we need a large power to be injected in relativistic protons as compared to that injected in electrons.," Since the VHE emission is basically determined by $pp$ interactions, we need a large power to be injected in relativistic protons as compared to that injected in electrons."655 This 1s because electrons cool completely. mainly by synchrotron emission. and protons undergo an important adiabatic cooling.," This is because electrons cool completely, mainly by synchrotron emission, and protons undergo an important adiabatic cooling."656 Hence. in the case of M87. we need a high value for the proton-to-electron power ratio: @=40.," Hence, in the case of M87, we need a high value for the proton-to-electron power ratio: $a=40$."657 A different. situation arisesfor Cen A. where the highest luminosities correspond to energies Ey<107eV. and the HE and VHE luminosities are comparatively lower.," A different situation arisesfor Cen A, where the highest luminosities correspond to energies $E_{\gamma}<10^7{\rm eV}$, and the HE and VHE luminosities are comparatively lower."658" In this case. We need (d.=2.5x1077) to allow the broadband electron-synchrotron spectrum to approximately account for all the data for E,«10'eV."," In this case, we need $a=2.5\times 10^{-2}$ ) to allow the broadband electron-synchrotron spectrum to approximately account for all the data for $E_{\gamma}<10^7{\rm eV}$."659 Then. for AA a lower luminosity in protons is enough to reach the level of the observed HE and VHE radiation through. proton-synchrotron and. pp interactions. respectively.," Then, for A a lower luminosity in protons is enough to reach the level of the observed HE and VHE radiation through proton-synchrotron and $pp$ interactions, respectively."660 A further difference between AA and M87 is in the slope of the injected particle distributions: for AA. we have a quite flat injection (s=1.8). while for M87 we find a steeper injection (s=2.4).," A further difference between A and M87 is in the slope of the injected particle distributions: for A, we have a quite flat injection $s=1.8$ ), while for M87 we find a steeper injection $s=2.4$ )."661 Also the acceleration efficiency ts greater for Cen A than for M87., Also the acceleration efficiency is greater for Cen A than for M87.662" This also has an impact in the neutrino spectrum produced. which for E,I TeV appears more difficult to be detected for M87 than for AA. Finally. we remark that a possible improvement of the present treatment. which is left for future work. should bethe inclusion of a time-dependent injection to account for flaring states."," This also has an impact in the neutrino spectrum produced, which for $E_\nu> 1 $ TeV appears more difficult to be detected for M87 than for A. Finally, we remark that a possible improvement of the present treatment, which is left for future work, should bethe inclusion of a time-dependent injection to account for flaring states."663 dz [p+]= 2p (ασπρο) £j. I. µία)- . S, dz (z) + ]= 2 dz z_0^2 ^2$\chi=\tan\xi_{\rm j}$ . ]. (664qrtA...,"z)- , ."665line profiles (due to higher spectral aud spatial resolution) which vield a FWIEMM of 170+20s.|.,"line profiles (due to higher spectral and spatial resolution) which yield a FWHM of $470\pm20\rm{km\,s^{-1}}$."666 Furthermore. they reported that the optical nucleus is displaced from the kinematical ceuter of the rotation curve by 1175 which corresponds to ppc.," Furthermore, they reported that the optical nucleus is displaced from the kinematical center of the rotation curve by $1\arcsec-1\farcs5$ which corresponds to pc."667 The Sevfert ealaxy 11386. was observed at ESO La Sila. Chile (Nov. 16. 1992) with the Casseerain Echelle Spectrograph (CASPEC) attached to the ESO 3.012. telescope.," The Seyfert galaxy 1386 was observed at ESO La Silla, Chile (Nov. 16, 1992) with the Cassegrain Echelle Spectrograph (CASPEC) attached to the ESO 3.6m telescope."668 The achieve spectral resolution with the short camera is R=MXAX18000 which corresponds to Av=Ἱτίπαν!|Í," The achieved spectral resolution with the short camera is $\mathrm{R}=\frac{\lambda}{\Delta\lambda}\approx 18000$ which corresponds to $\Delta v = 17\,\mathrm{km\,s^{-1}}$."669 With the use of the red cross-disperser the echelle spectzuii covers he rangeA., With the use of the red cross-disperser the echelle spectrum covers the range.670". The slit covered an area of 8""&17 and was orieuted at p.a. 167", The slit covered an area of $8\arcsec \times1\arcsec$ and was oriented at p.a. $16\degr$.671" The CCD chip. a 5512M.12 with 512« pixels of 27,nu pix.+ offers a spatial scale of 0765pixt."," The CCD chip, a 512M–12 with $512\times512$ pixels of $\mu$ $\rm{pix}^{-1}$ offers a spatial scale of $\rm{0\farcs65\,pix^{-1}}$."672 The 11386 spectrum bad an iutegratiou time of sec., The 1386 spectrum had an integration time of sec.673 The data reduction was performed with the and softwareJ packages., The data reduction was performed with the and software packages.674 TheY spectruui was bias: corrected creating a master bias which was subtracted from the spectrin., The spectrum was bias corrected creating a master bias which was subtracted from the spectrum.675 The tracing was cletermined from standard star exposures., The tracing was determined from standard star exposures.676 Iu this xocess a Chebychey polynomial of 3°! order was fitted. along he dispersion axis of cach aperture., In this process a Chebychev polynomial of $3^{\mathrm{rd}}$ order was fitted along the dispersion axis of each aperture.677 The master trace was defined by the spectrum with the smallest rius deviations., The master trace was defined by the spectrum with the smallest rms deviations.678 The echelle PAoectrumi was then background corrected making use of 16 iuterorder sections of the 2D echelle spectrograin., The echelle spectrum was then background corrected making use of the interorder sections of the 2D echelle spectrogram.679 The fatfielc correction was doue ini two cifferent y.eps., The flatfield correction was done in two different steps.680 Due to spatial offsets aud differcut slit leneths. we iad to create several groupso of flatfields.," Due to spatial offsets and different slit lengths, we had to create several groups of flatfields."681 The internal scatter of the spatial offsets was less than lppix within a flatfield exoup., The internal scatter of the spatial offsets was less than pix within a flatfield group.682 The deviation between he individual Hatfield eroups had offsets of the οτίer of Ayz ppix., The deviation between the individual flatfield groups had offsets of the order of $\Delta y \approx$ pix.683 For cach group a normalized fatiield was computed which were used to correct for overall seusitivitv variations of the corresponding scicuce frames., For each group a normalized flatfield was computed which were used to correct for overall sensitivity variations of the corresponding science frames.684 Due to the flexure of the spectrograph the echelle object spectra had s1all offsets with respect to the correspondius Zatfold exposure., Due to the flexure of the spectrograph the echelle object spectra had small offsets with respect to the corresponding flatfield exposure.685 IIence. we were forced to restrict he 2D datfield correction to the inuer while the 1755 wide stripes above au below this region were not corrected in this step.," Hence, we were forced to restrict the 2D flatfield correction to the inner while the 5 wide stripes above and below this region were not corrected in this step."686 The normalized flatficeld was set to unity for the region of these stripes., The normalized flatfield was set to unity for the region of these stripes.687 The exiteriuu for the selection of these scans based on au iutensitv of less than zz50 scan., The criterium for the selection of these scans based on an intensity of less than $\approx$ scan.688" In the second step the final extractec LD spectra of the inner 6""of the individual spatial scans were flatfield corrected with a ID flatfield generated.", In the second step the final extracted 1D spectra of the inner of the individual spatial scans were flatfield corrected with a 1D flatfield generated.689 It was created by normalizing the individual scans of the usec flatficlel for the 2D correction with the average 1D datiield of it., It was created by normalizing the individual scans of the used flatfield for the 2D correction with the average 1D flatfield of it.690 Finally we are able to make use of the 2D echelle spectrograms covering the NLR eas of 11386 out to a radius of zz37 from the nucleus., Finally we are able to make use of the 2D echelle spectrograms covering the NLR gas of 1386 out to a radius of $\approx3\arcsec$ from the nucleus.691 Subsequently the data were waveleneth calibrated by using a ThaAr lamp reference spectrum., Subsequently the data were wavelength calibrated by using a ThAr lamp reference spectrum.692 The unit step was set toOLIGLA., The unit step was set to.693. The scatter of our wavelength calibration had an rmm ofO., The scatter of our wavelength calibration had an rms of.694OLLA.. The spectral resolution of our spectra was obtained from measurements of several nightsky lines in our spectra aud was fouud to beO., The spectral resolution of our spectra was obtained from measurements of several night--sky lines in our spectra and was found to be.6953A.. A final flux calibration was applied using the standard 323151 G4 να) which was reduced in the same vay as the 2-D spectrum of 11386., A final flux calibration was applied using the standard 3454 $\eta$ Hya) which was reduced in the same way as the 2-D spectrum of 1386.696 The extraced spectrin was fually merece and a two-dimensional image was created from the 11 pixel scans., The extracted spectrum was finally merged and a two-dimensional image was created from the 11 pixel scans.697 Tocorrect or the effect of slit illumination. we divided our 2-D galaxy echellespectrogram by au ideutically processed nonnualized skyflatficlel exposure.," Tocorrect for the effect of slit illumination, we divided our 2-D galaxy echelle--spectrogram by an identically processed normalized sky--flatfield exposure."698 Finally a cosmices correction was applied to the spectrum using the MIDAS routine., Finally a cosmics correction was applied to the spectrum using the MIDAS routine.699 In Fie., In Fig.700 2 we present the spectra of 11386 from the ceutral 2G., \ref{F2} we present the spectrum of 1386 from the central $2\farcs6$.701" The typical strong emission lines of Sevfert galaxies. Πα, [Nui]. uj are visible."," The typical strong emission lines of Seyfert galaxies, $\alpha$, ], ] are visible."702 Above the ρου dis dominated by strong atmospheric absorption bauds (b-band. A-band).," Above the spectrum is dominated by strong atmospheric absorption bands (b-band, A-band)."703 We retrieved high resolution images of 11386 from the Space Telescope Scicuce Institute (STScL) data archive (frou the survey by Malkau et al. 1998.. ," We retrieved high resolution images of 1386 from the Space Telescope Science Institute (STScI) data archive (from the survey by Malkan et al. \cite{MGT}, ,"70455179)., 5479).705Abell 2052 has been observed with XMM-Newton in two observation campaigns.,Abell 2052 has been observed with XMM-Newton in two observation campaigns.706 Two observations have been performed in 2000 with a total exposure time of 37 ks and another ten exposures were obtained in 2007 with a total observing time of 22] ks., Two observations have been performed in 2000 with a total exposure time of 37 ks and another ten exposures were obtained in 2007 with a total observing time of 221 ks.707 The event files for the MOS and pi detectors are re-produced using the standard SAS 9.0.0 pipeline tools., The event files for the MOS and pn detectors are re-produced using the standard SAS 9.0.0 pipeline tools.708 In order to reduce the soft-proton background. we filter the data with a 10-12 keV count-rate threshold.," In order to reduce the soft-proton background, we filter the data with a 10–12 keV count-rate threshold."709 We determine the threshold for the 2000 (AOI) and 2007 (AO4) data separately., We determine the threshold for the 2000 (AO1) and 2007 (AO4) data separately.710 For the AO4 data we combined all the separate observations to obtain one 10-12 keV light curve per instrument., For the AO4 data we combined all the separate observations to obtain one 10-12 keV light curve per instrument.711 A count-rate histogram created from this light curve with 100 s wide bins is fitted with a Gaussian to determine the count rate of the quiescent emission (V)., A count-rate histogram created from this light curve with 100 s wide bins is fitted with a Gaussian to determine the count rate of the quiescent emission $N$ ).712 We then define the minimum and maximum count rate (7) to be T=N+3VN. which is the 3c deviation from the Poissonian mean.," We then define the minimum and maximum count rate $T$ ) to be $T = N~\pm~3\sqrt{N}$, which is the $\sigma$ deviation from the Poissonian mean."713 We apply this to both the AOI and AO4 data sets., We apply this to both the AO1 and AO4 data sets.714 For the AOI data. we obtain allowed count rates in the range 0.01-0.18 (MOS1). 0.01-0.18 (MOS2). and 0.11—0.43 (pn) in units counts s.," For the AO1 data, we obtain allowed count rates in the range 0.01–0.18 (MOS1), 0.01–0.18 (MOS2), and 0.11–0.43 (pn) in units counts $^{-1}$."715 The average rate in counts ! in the AO4 data was somewhat higher: 0.03- (MOSI). 0.04—0.28 (MOS2). and 0.28-0.70 (pr).," The average rate in counts $^{-1}$ in the AO4 data was somewhat higher: 0.03--0.27 (MOS1), 0.04–0.28 (MOS2), and 0.28–0.70 (pn)."716 This ts due to the secular evolution of the XMM-Newton instrumental background., This is due to the secular evolution of the XMM-Newton instrumental background.717 In Table 1.. we list all used observations of with their respective exposure times after filtering for flares.," In Table \ref{tab:exposure}, we list all used observations of with their respective exposure times after filtering for flares."718 Two other observations are discarded. because the count rate was above the threshold during the entire exposure.," Two other observations are discarded, because the count rate was above the threshold during the entire exposure."719 Only eight of the brightest point sources in the field were selected by eve using a combined image of MOS and pn., Only eight of the brightest point sources in the field were selected by eye using a combined image of MOS and pn.720" Regions with a radius of 15"" around these sources were subsequently excluded from the data set.", Regions with a radius of $^{\prime\prime}$ around these sources were subsequently excluded from the data set.721 In order to resolve structures in. temperature and iron abundance. we divide the data in small regions from which spectra can be extracted.," In order to resolve structures in temperature and iron abundance, we divide the data in small regions from which spectra can be extracted."722 To obtain sufficient signal-to-noise per spatial bin. we use the Weighted Voronoi Tessellation (WVT) binning algorithm by ?.. which is a generalization of the ? Voronot binning algorithm.," To obtain sufficient signal-to-noise per spatial bin, we use the Weighted Voronoi Tessellation (WVT) binning algorithm by \citet{diehl2006}, which is a generalization of the \citet{cappellari2003} Voronoi binning algorithm."723 We apply the binning to the total background subtracted image and create maps with a signal-to-noise of 150c per bin., We apply the binning to the total background subtracted image and create maps with a signal-to-noise of $\sigma$ per bin.724 Because of the relatively low surface brightness of the source compared to the X-ray background in the outer parts of the cluster. we only select bins within a radius of 4' (~ 168 kpe) around the centre of the central cD galaxy.," Because of the relatively low surface brightness of the source compared to the X-ray background in the outer parts of the cluster, we only select bins within a radius of $^{\prime}$ $\sim$ 168 kpc) around the centre of the central cD galaxy."725 For every bin. we extract the event files and spectra.," For every bin, we extract the event files and spectra."726 Then. we calculate the response matrices and effective area files for all spatial bins using one AOI pointing and one AO4 pointing.," Then, we calculate the response matrices and effective area files for all spatial bins using one AO1 pointing and one AO4 pointing."727 These response and effective area files are also used for the other pointings of the same AO in order to reduce computing time., These response and effective area files are also used for the other pointings of the same AO in order to reduce computing time.728 We checked that the response is stable enough within one AO., We checked that the response is stable enough within one AO.729 Also. the pointings within one AO were very similar. causing the extraction regions defined in WCS coordinates to cover the same area in detector coordinates for every pointing.," Also, the pointings within one AO were very similar, causing the extraction regions defined in WCS coordinates to cover the same area in detector coordinates for every pointing."730 Therefore. using one response matrix per spatial bin per AO is justified.," Therefore, using one response matrix per spatial bin per AO is justified."731 As we are mainly interested in relative differences between bins. we adopt a relatively simple background treatment for the maps.," As we are mainly interested in relative differences between bins, we adopt a relatively simple background treatment for the maps."732 We subtract a scaled filter wheel closed spectrum from the source spectrum., We subtract a scaled filter wheel closed spectrum from the source spectrum.733 The scaling factor is based on the out-of-field-of-view events in MOS., The scaling factor is based on the out-of-field-of-view events in MOS.734 The spectra for each bin are fitted simultaneously using the SPEX spectral fitting package., The spectra for each bin are fitted simultaneously using the SPEX spectral fitting package.735 The Cosmic X-ray Background (CXB) is included as a set of model components in the fit., The Cosmic X-ray Background (CXB) is included as a set of model components in the fit.736 For the Ny we use the Galactic value of Dx 107 em (?).., For the $N_{\mathrm{H}}$ we use the Galactic value of $\times$ $^{20}$ $^{-2}$ \citep{kalberla2005}.737 Apart from spectra extracted from binned maps. we also carefully analyse spectra extracted from certain interesting regions that we identify in the maps.," Apart from spectra extracted from binned maps, we also carefully analyse spectra extracted from certain interesting regions that we identify in the maps."738 In addition. the parameters of the CXB components need to be estimated. because they are needed for fitting the maps.," In addition, the parameters of the CXB components need to be estimated, because they are needed for fitting the maps."739 Therefore. we use a separate procedure for these high signal-to-noise spectra.," Therefore, we use a separate procedure for these high signal-to-noise spectra."740 The background treatment is very important when fitting spectra extracted from the outer regions of a cluster. where the flux of the cluster emission is comparable to the background.," The background treatment is very important when fitting spectra extracted from the outer regions of a cluster, where the flux of the cluster emission is comparable to the background."741 Correcting for all the various background components in XMM-Newton data is very challenging. because maiv components either depend on the position on the sky or depend on the epoch of observation.," Correcting for all the various background components in XMM-Newton data is very challenging, because many components either depend on the position on the sky or depend on the epoch of observation."742 The fact that we have obtained a lot of relatively short exposures with different background conditions. demands a careful treatment of all the components.," The fact that we have obtained a lot of relatively short exposures with different background conditions, demands a careful treatment of all the components."743 Although there are very well constructed methods like. for example. ?.. there are a number of drawbacks when they are applied to this data set.," Although there are very well constructed methods like, for example, \citet{snowden2008}, there are a number of drawbacks when they are applied to this data set."744 The success of these methods strongly depends on the events registered outside the XMM-Newton field of view., The success of these methods strongly depends on the events registered outside the XMM-Newton field of view.745 Because the pn instrument has very small out-of-field-of-view regions. their method is practically unusable for pn data.," Because the pn instrument has very small out-of-field-of-view regions, their method is practically unusable for pn data."746 Secondly. the amount of counts in the out-of-field of view regions is rather small for short exposure times. which puts a relatively large uncertainty on the derived scaling factor for the instrumental background.," Secondly, the amount of counts in the out-of-field of view regions is rather small for short exposure times, which puts a relatively large uncertainty on the derived scaling factor for the instrumental background."747 This drawback can be avoided by stacking event files. but only if the gain and background were similar during the observations.," This drawback can be avoided by stacking event files, but only if the gain and background were similar during the observations."748 Here.," Here,"7493 11.5 eV. for the expoucutial fit oot: 03) for 19 d.o.£).,$\pm$ 1.5 eV for the exponential fit of 0.39 for 19 d.o.f.).750 When fitting the decay curve with a powerlaw. we found paramcter values οἳ 22.5 eV and + 00.003 oof 0.51 for 20 d.o.£).," When fitting the decay curve with a power-law, we found parameter values of $\pm$ 2.5 eV and $\pm$ 0.003 of 0.51 for 20 d.o.f.)."751 Iun sununiurw. the best-fit values obtained when Chandra aud Suvft values are taken into account are cousistent within the errors with the values obtained oulv with the vvalues.," In summary, the best-fit values obtained when $Chandra$ and $Swift$ values are taken into account are consistent within the errors with the values obtained only with the values."752 We note that we took the Chandra and Suvft values from ?.. who fixed the mass of the NS to 1.1 M. aud the distance to to T.1l kpc in their fits.," We note that we took the $Chandra$ and $Swift$ values from \citet{0748:degenaar10mnras}, who fixed the mass of the NS to 1.4 $\Msun$ and the distance to to 7.4 kpc in their fits."753 Although we fixed the nass of he NS to its best-fit value of 1.75 M. aud the cistauce ο T.l kpe to obtain the opoiuts. Table 1 shows that the temperature values are consisteut within the errors for a mass of 1.78 AL. (Case 1) and Lt AL. (Case 5).," Although we fixed the mass of the NS to its best-fit value of 1.78 $\Msun$ and the distance to 7.1 kpc to obtain the points, Table \ref{tab:epic-all-trials} shows that the temperature values are consistent within the errors for a mass of 1.78 $\Msun$ (Case 4) and 1.4 $\Msun$ (Case 5)."754 In addition. Table 3 shows jit increasing the distance from 7.1 to 8.3 προ causes sienificant changes in the values of the mass aud radius of 16 NS but not in the effective temperature.," In addition, Table \ref{tab:fit-sim} shows that increasing the distance from 7.1 to 8.3 kpc causes significant changes in the values of the mass and radius of the NS but not in the effective temperature."755 This explains rat we obtain consistent decay curves when the Chandra and Savff values are included in the fit., This explains that we obtain consistent decay curves when the $Chandra$ and $Swift$ values are included in the fit.756 We attribute 1ο siuall errors of the Chandra points compared to the opoiuts (despite the poorer quality of the Chandra spectra) to the fact that ? fixed all the parameters ofthe fit except the effective temperature aud the normalisation of the power-law component., We attribute the small errors of the $Chandra$ points compared to the points (despite the poorer quality of the $Chandra$ spectra) to the fact that \citet{0748:degenaar10mnras} fixed all the parameters of the fit except the effective temperature and the normalisation of the power-law component.757 Therefore. the added. value of the Chandra aud Suift points should be taken with caution.," Therefore, the added value of the $Chandra$ and $Swift$ points should be taken with caution."758 We extracted images from the UVW1. UVA and UVW2 filter OM exposures for Obs 1.," We extracted images from the UVW1, UVM2 and UVW2 filter OM exposures for Obs 1."759 Based on the expected decreasing optical maenitude of the source. we chose to perform: Obs 2L onlv with the U filter to maximise the sensitivity.," Based on the expected decreasing optical magnitude of the source, we chose to perform Obs 2–4 only with the U filter to maximise the sensitivity."760 OM data were not available for Obs 3 due to a technical error., OM data were not available for Obs 3 due to a technical error.761 For Obs 2 and E sve extracted images and light curves for all OM exposures., For Obs 2 and 4 we extracted images and light curves for all OM exposures.762" The images show a source consistent with the position of wwhich fades from Obs 1: to 1,", The images show a source consistent with the position of which fades from Obs 1 to 4.763 Tn Obs 1. we obtained au average magnitude of d: 00.1 in the UVWT filter.," In Obs 1, we obtained an average magnitude of $\pm$ 0.1 in the UVW1 filter."764 The source was not detecte in the UVM?2 or UVW2 filters., The source was not detected in the UVM2 or UVW2 filters.765" For Obs 2 and [sve obtained average U optical magnitudes of 411.8 and 435.2. respectively,"," For Obs 2 and 4 we obtained average U optical magnitudes of $\pm$ 1.8 and $\pm$ 3.2, respectively."766 We note that iis not detected in 1 out of LO exposures in Obs 2 and in ll out of 19 exposures in Obs f., We note that is not detected in 4 out of 10 exposures in Obs 2 and in 14 out of 19 exposures in Obs 4.767 Fig., Fig.768 6 shows the detections du all observations as a function of phase., \ref{fig:om} shows the detections in all observations as a function of phase.769 Clearly. the optical magnitude was still decreasing in Obs 4 compared to Obs 2.," Clearly, the optical magnitude was still decreasing in Obs 4 compared to Obs 2."770 Unfortunately the errors are too large since the source is falling below detectability with OAL, Unfortunately the errors are too large since the source is falling below detectability with OM.771 Therefore. we cannot determine the presence of a modulation with orbital phase.," Therefore, we cannot determine the presence of a modulation with orbital phase."772 We analysed four oobservations of sspanline 19 mouths aud starting in November 2008. when a significant halt of accretion iuto the NS was detected.," We analysed four observations of spanning 19 months and starting in November 2008, when a significant halt of accretion into the NS was detected."773setup Sphl and Ell): Asse»= 57. ντε.=30 (for setup Sph2 and setup Ell2).,"setup Sph1 and Ell1); $\mathcal{M}_{S2E2}=57$ , $\chi_{S2E2}=30$ (for setup Sph2 and setup Ell2)."774 According to ?) (Fig., According to \citet{opr05} (Fig.775 2). for these values radiative cooling dominates over thermal conduction.," 2), for these values radiative cooling dominates over thermal conduction."776 This implies the local formation of thermal instabilities in structures with dimensions L>Ly=1.310°77/n (Ly~10!° em. for T=2x10° K and -5 em? which is the critical Field length (?)).," This implies the local formation of thermal instabilities in structures with dimensions $L>L_{F}=1.3\times 10^{6}T^{2}/n$ $L_{F}\sim10^{16}$ cm, for $T=2\times10^{5}$ K and $n=5$ $^{-3}$ ), which is the critical Field length \citealt{fie65}) )."777" Notice. however. that the results reported in ?) were derived for an impact of a SNR shock with a spherical cloud with radius R=3.09x1015 em. while our clouds are smaller,"," Notice, however, that the results reported in \citet{opr05} were derived for an impact of a SNR shock with a spherical cloud with radius $R=3.09\times10^{18}$ cm, while our clouds are smaller."778 So we expect lower values of the characteristic length of temperature variations /; in our simulations., So we expect lower values of the characteristic length of temperature variations $l_{T}$ in our simulations.779 Since the characteristic conductive time-scale 15 smaller clouds imply a higher efficiency. of thermal conduction. which may inhibit the formation of thermal instabilities.," Since the characteristic conductive time-scale is smaller clouds imply a higher efficiency of thermal conduction, which may inhibit the formation of thermal instabilities."780 The simulations are performed 1n. a. cylindrical 2-D coordinate system ος z) assuming axial symmetry.," The simulations are performed in a cylindrical 2-D coordinate system $r,~ z$ ), assuming axial symmetry."781 The computational domain extends over 1.5x10!’ em in the + direction and over 2x10? em in the z direction., The computational domain extends over $1.5\times10^{19}$ cm in the $r$ direction and over $2\times10^{19}$ cm in the $z$ direction.782 We use reflection boundary conditions at r.=0 and zero-gradient boundary conditions (for v. p. and p) elsewhere.," We use reflection boundary conditions at $r=0$ and zero-gradient boundary conditions (for $\bf{v}$, $\rho$, and $p$ ) elsewhere."783 The shock velocity is parallel to the z axis. which corresponds to the North direction in the observation analyzed in Paper I. The post-shock initial conditions are given in the strong shock limit (2)).," The shock velocity is parallel to the $z$ axis, which corresponds to the North direction in the observation analyzed in Paper I. The post-shock initial conditions are given in the strong shock limit \citealt{zr67}) )."784 The finest spatial resolution is ~1.95x10!? em. therefore we have more than 100 zones per cloud radius in setup Sphl and Sph2 and 2150 and 250 zones per semimajor and semiminor axis. respectively. in setup Ell! and EID.," The finest spatial resolution is $\sim1.95\times10^{16}$ cm, therefore we have more than 100 zones per cloud radius in setup Sph1 and Sph2 and $\ga150$ and $\ga 50$ zones per semimajor and semiminor axis, respectively, in setup Ell1 and Ell2."785 Our modeling allows us to simulate the detailed evolution of the temperature and density of the shock-cloud system., Our modeling allows us to simulate the detailed evolution of the temperature and density of the shock-cloud system.786 From the computed temperature and density we are able to synthesize the X-ray emission detectable with the MOS| camera (?))., From the computed temperature and density we are able to synthesize the X-ray emission detectable with the EPIC-MOS1 camera \citealt{taa01}) ).787 By rotating the 2D maps of » and 7 about the symmetry axis. we obtain the full 3D distributions inthe cartesian space (V.V. z). where the Y. axis corresponds to the direction of the line of sight and is perpendicular to the ο.5) plane.," By rotating the 2D maps of $n$ and $T$ about the symmetry axis, we obtain the full 3D distributions inthe cartesian space $x',~y',~z'$ ), where the $y'$ axis corresponds to the direction of the line of sight and is perpendicular to the $(r,~z)$ plane."788 We then derive the emission measure. Ελα”.ν΄. z).," We then derive the emission measure, $EM(x',~y',~z')$ ,"789These models are summarized in Table 2..,These models are summarized in Table \ref{fits}.790 For each model. we look al the statistical distributions of the best-fit parameters of our 10.000 realizations.," For each model, we look at the statistical distributions of the best-fit parameters of our $10,000$ realizations."791 We find that the distributions are roughly Gaussian wilh means (hat approximately equal the underlying simulation values., We find that the distributions are roughly Gaussian with means that approximately equal the underlying simulation values.792 We concern ourselves with the standard deviations. which are representative of the errors (o be expected [rom peculiar velocities in each scenario.," We concern ourselves with the standard deviations, which are representative of the errors to be expected from peculiar velocities in each scenario."793 To check our results. we will use (wo auxiliary methods for estimating (he parameter errors.," To check our results, we will use two auxiliary methods for estimating the parameter errors."794" The first method involves generating ""svnthetic survey data. wherein we do not use the N-body data but instead we choose the velocities at random [rom a Gaussian distribution with the known variance (02)."," The first method involves generating “synthetic"" survey data, wherein we do not use the N-body data but instead we choose the velocities at random from a Gaussian distribution with the known variance $\langle v^2 \rangle$."795 Then. proceeding as before. we will find the contribution to the error that is due solely to uncorrelated noise. ie. we will find (he first termi in equation (3)).," Then, proceeding as before, we will find the contribution to the error that is due solely to uncorrelated noise, i.e. we will find the first term in equation \ref{error}) )."796" Secondly. we can estimate Fisher matrices (II&Greene2006).. where C;;=(Omdm;). po=(h.OQ3,.etc.). and the error in parameter p, is F1."," Secondly, we can estimate Fisher matrices \citep{HG}, where $\tilde{C}_{ij}=\langle\delta m_i\delta m_j\rangle$, $p_{\alpha}=(h,\Omega_M,{\rm etc.})$, and the error in parameter $p_{\alpha}$ is $\sigma_{\alpha}=\sqrt{[F^{-1}]_{\alpha\alpha}}$ ."797" The Fisher matrices provide a useful check of our code. and they also give us an analviic understanding of the scaling of the uncorrelated errors with No and z444 for each case,"," The Fisher matrices provide a useful check of our code, and they also give us an analytic understanding of the scaling of the uncorrelated errors with $N$ and $z_{\rm max}$ for each case."798" We will then fit the finalvariances as 67,4σρωTocue Where σρως 15 Che uncorrelated component of the error and 64,4 is the correlated component."," We will then fit the finalvariances as $\sigma_{\rm total}^2=\sigma_{\rm pois}^2+\sigma_{\rm corr}^2$, where $\sigma_{\rm pois}$ is the uncorrelated component of the error and $\sigma_{\rm corr}$ is the correlated component."799" We expect (hat o5, scales as L/v.N. and both oy, and o, are power laws 1n zy, for twas«1."," We expect that $\sigma_{\rm pois}$ scales as $1/\sqrt{N}$ , and both $\sigma_{\rm pois}$ and $\sigma_{\rm corr}$ are power laws in $z_{\rm max}$ for $z_{\rm max}\ll 1$."800 Hence. we expect thepep formd of.) =DM Aou2muUN+NTPADBri.forsmall2.b 244; ⋅Uhis ⋅expectation↽↽ comes. from2d errorsthe offindings of Vanderveld et al. (," Hence, we expect errors of the form $\sigma_{\rm total}^2=Az_{\rm max}^a/N+Bz_{\rm max}^b$ for small $z_{\rm max}$; this expectation comes from the findings of Vanderveld et al. ("8012007). Section VB.,"2007), Section VB."802 For model (1). with τμ=0. we show some of our results in Table 3..," For model (i), with $z_{\rm min}=0$, we show some of our results in Table \ref{2param}."803" [ere o; is the standard deviation of the errors in A amd oy; is (he corresponding error in δα, where we are only considering the errorsdue to peculiar velocities."," Here $\sigma_h$ is the standard deviation of the errors in $h$ and $\sigma_M$ is the corresponding error in $\Omega_M$ , where we are only considering the errorsdue to peculiar velocities."804 These results are best [it by ↓⊇⇀, These results are best fit by and805 These results are best [it by ↓⊇⇀↴, These results are best fit by and806 These results are best [it by ↓⊇⇀↴↖, These results are best fit by and807 These results are best [it by ↓⊇⇀↴↖⋡, These results are best fit by and808 These results are best [it by ↓⊇⇀↴↖⋡↓, These results are best fit by and809 These results are best [it by ↓⊇⇀↴↖⋡↓⋗, These results are best fit by and810 These results are best [it by ↓⊇⇀↴↖⋡↓⋗⊾, These results are best fit by and811The racial velocities of the P-type secondary star in Nova Seo 1994 were measured from the spectra by the method of cross-correlation (Tonry Davis 1979) with a template star.,The radial velocities of the F-type secondary star in Nova Sco 1994 were measured from the spectra by the method of cross-correlation (Tonry Davis 1979) with a template star.812 Prior to cross-correlation the spectra were interpolated onto a logarithmic wavelength scale (pixel size 55 1)) using a sin.rf.r interpolation scheme to minimize data smoothing (Stover et al.," Prior to cross-correlation the spectra were interpolated onto a logarithmic wavelength scale (pixel size 55 ) using a $\sin\,x/x$ interpolation scheme to minimize data smoothing (Stover et al."813 1980). and then normalised.," 1980), and then normalised."814 The template star spectrum (LER2906: E6060) was then artificially broadened by 90 t(Shahbaz et al..," The template star spectrum (HR2906; $\sc v$ ) was then artificially broadened by 90 (Shahbaz et al.,"815 1999) to account for the rotational velocity of the secondary star., 1999) to account for the rotational velocity of the secondary star.816 Note that the orbital smearing of the Nova Seo 1994 spectra through the LSO0s exposure is at most only 10+. much less than the resolution of the data.," Note that the orbital smearing of the Nova Sco 1994 spectra through the 1800s exposure is at most only 10, much less than the resolution of the data."817 Only regions of the spectrum devoid of emission lines (6400-6520.A)) were used in the eross-correlation., Only regions of the spectrum devoid of emission lines ) were used in the cross-correlation.818 The raclia velocity of the template star (derived. using the position of the Ho absorption line to be 7 13) was then adde to the radial velocities of Nova Seo 1994., The radial velocity of the template star (derived using the position of the $\alpha$ absorption line to be $-$ 7 ) was then added to the radial velocities of Nova Sco 1994.819 Using the orbital ephemeris given by van der Hooft e al (1998) we phase-folded and binned the heliocentric raclia velocities (sec Figure 2)., Using the orbital ephemeris given by van der Hooft et al (1998) we phase-folded and binned the heliocentric radial velocities (see Figure 2).820 From figure 2. it can be seen tha the radial velocity measurement at phase 0.2 does not fit the general pattern of the sinusoidal modulation present in the data.," From figure 2, it can be seen that the radial velocity measurement at phase 0.2 does not fit the general pattern of the sinusoidal modulation present in the data."821 This data point was the total of three radial velocity measurements taken on the second night (21st June 1996)., This data point was the total of three radial velocity measurements taken on the second night (21st June 1996).822 Although the seeing and quality of the spectra taken during this night were not as good as the others. no obvious reason could. be found as to why these spectra gave much lower radial velocities than expected.," Although the seeing and quality of the spectra taken during this night were not as good as the others, no obvious reason could be found as to why these spectra gave much lower radial velocities than expected."823 A sine wave fit to all the data points does not give an adequate fit (456.9)., A sine wave fit to all the data points does not give an adequate fit $\chi^{2}_{\nu}$ =6.9).824" Llowever, removing the discrepant data point and then performing a sine wave fit vields a X7; of 1.5. a semi-amplitude A»=279+10 . svstemic. velocity. 5=——155c-7 and a phase shift of 0.043+0.0056 (1-0 errors are given)."," However, removing the discrepant data point and then performing a sine wave fit yields a $\chi^{2}_{\nu}$ of 1.5, a semi-amplitude $K_{2}=279 \pm 10$ , systemic velocity $\gamma=-155 \pm 7$ and a phase shift of $-0.043 \pm 0.005 \phi$ $\sigma$ errors are given)."825 We also fitted the racial velocity curve with an eccentric orbit. but found the fit to be less than 50 percent significant.," We also fitted the radial velocity curve with an eccentric orbit, but found the fit to be less than 50 percent significant."826 Three absorption line radial velocity. curves have. been obtained for Nova Seo 1994. using the same absorption features of the Gir secondary star and the standard moetlioc ol eross-correlation.," Three absorption line radial velocity curves have been obtained for Nova Sco 1994, using the same absorption features of the $\sc iv$ secondary star and the standard method of cross-correlation."827 However. in cach case the system was observed. to be in a cillerent N-rav. state.," However, in each case the system was observed to be in a different X-ray state."828 A sinusoidal fi to the outhurst data taken in April/May 1995 of Orosz Dailvn (1998) gives a radial velocity semi-amplituce Of ΟΕοι., A sinusoidal fit to the outburst data taken in April/May 1995 of Orosz Bailyn (1998) gives a radial velocity semi-amplitude of $K_{obs}$ $\pm 2$.829 During this period BALSE cli not detect the source. so we can only put an upper lini of 24.10% («0.03 photons erg cm7? + in the BATSE 20-350 keV energy range) to the X-ray luminosity of the source.," During this period BATSE did not detect the source, so we can only put an upper limit of $\times$ $^{36}$ $<$ 0.03 photons erg $^{-2}$ $^{-1}$ in the BATSE 20-350 keV energy range) to the X-ray luminosity of the source."830 This upper limit alone does not allow us to state unequivocally that the source was not active at X-ray energies. but optical observations suggest that the source was not in quiescence (V=16.5: Orosz Bailyn 1998).," This upper limit alone does not allow us to state unequivocally that the source was not active at X-ray energies, but optical observations suggest that the source was not in quiescence $V$ =16.5; Orosz Bailyn 1998)."831" In section 4 we determined Ao=279+10kms from data taken in June 1996 when INTE ASAI (2-12 keV) observations give an N-rav luminosity of L,—6.8 1071. and the A- band brightness was  1 mag brighter than its quiescent value."," In section 4 we determined $K_2$ $\pm10$ from data taken in June 1996 when RXTE ASM (2-12 keV) observations give an X-ray luminosity of $L_x$ $\times$ $^{37}$, and the $R$ -band brightness was $\sim$ 1 mag brighter than its quiescent value."832 The D.NISE (20350 keV) count rate was at least a [actor of 4 higher than in April/May 1995., The BATSE (20–350 keV) count rate was at least a factor of 4 higher than in April/May 1995.833 Shahbaz et al. (, Shahbaz et al. (8341999) determined the true radial velocitv of the secondary star (A5—215.532.4 1)) in 1998 MavJune. when the source was finally in optical quiescence.,"1999) determined the true radial velocity of the secondary star $K_2$ $\pm2.4$ ) in 1998 May/June, when the source was finally in optical quiescence."835 The only X-ray quiescent observations were obtained during March. 1996 using ASC'A (1-10 keV: Robinson et al.," The only X-ray quiescent observations were obtained during March 1996 using ASCA (1-10 keV; Robinson et al.,"836" LOOT) which gave L,—2. 107Ll.", 1997) which gave $L_x$ $\times$ $^{32}$.837 In Figure 3 we show the observed radial velocity amplitudes relative to the quiescent value as a function of the observed X-ray luminosity at the time of the measurements., In Figure 3 we show the observed radial velocity amplitudes relative to the quiescent value as a function of the observed X-ray luminosity at the time of the measurements.838 We have converted. the N-rav luminosities. which were observed with dillerent instruments. into a common energv range (0.410 keV) using a hydrogen column density of Ny20.809.1077 7; and à photon power-law model with. indices 2.8 and 1.5 for the N-rav. high ancl quiescent states respectively (see Table 3: Zhang et al.," We have converted the X-ray luminosities, which were observed with different instruments, into a common energy range (0.4–10 keV) using a hydrogen column density of $N_h=0.89\times 10^{22}$ $^{-2}$ and a photon power-law model with indices 2.8 and 1.5 for the X-ray high and quiescent states respectively (see Table 3; Zhang et al.,"839 1997: Robinson et al..," 1997; Robinson et al.,"840 1997: Lameury et al.," 1997; Hameury et al.,"841 1997)., 1997).842 This energy range is where we expect the total ractiatecl power for X-ray transients in both outburst and quiescence to lic (Chen. Shrader Livio 1997).," This energy range is where we expect the total radiated power for X-ray transients in both outburst and quiescence to lie (Chen, Shrader Livio 1997)."843 ote that there is a correlation between X-ray. luminosity and the observed racial velocity semi-amplitude: the higher he X-ray luminosity the larger the observed radial velocity semi-amplitude. exactIy as expected.," Note that there is a correlation between X-ray luminosity and the observed radial velocity semi-amplitude; the higher the X-ray luminosity the larger the observed radial velocity semi-amplitude, exactly as expected."844 We can use our model ο estimate the X-ray luminosity at the time when Orosz Dailvn (1997) took their radial velocity measurements., We can use our model to estimate the X-ray luminosity at the time when Orosz Bailyn (1997) took their radial velocity measurements.845" We find L,~5«10% which is consistent with the BATSE upper limit.", We find $L_{x} \sim 5\times 10^{35}$ which is consistent with the BATSE upper limit.846 lt has been known for some time. especially in studies of dwarf novae ancl polars. that substantial heating of the secondary star shifts the effective centre of the secondary. weighted by the strength of the absorption lines. from the centre of mass of the star.," It has been known for some time, especially in studies of dwarf novae and polars, that substantial heating of the secondary star shifts the effective centre of the secondary, weighted by the strength of the absorption lines, from the centre of mass of the star."847 This results in a significant distortion of the radial velocity curve leading to a spuriously high semi-amplitude and a racial velocity curve that may be eccentric., This results in a significant distortion of the radial velocity curve leading to a spuriously high semi-amplitude and a radial velocity curve that may be eccentric.848 Davey Smith (1992) describe a procedure for detecting the ellects of irradiation on the racial velocity curve of the secondary star. whereby. one tests the significance of an eccentricity in the orbital. solution.," Davey Smith (1992) describe a procedure for detecting the effects of irradiation on the radial velocity curve of the secondary star, whereby one tests the significance of an eccentricity in the orbital solution."849 Llowever. it should be noted that. although our data does not allow this eccentricity test. due to the poor orbital phase coverage. we can use the spuriously high racial velocity amplitude to show that N-rav heating is present.," However, it should be noted that, although our data does not allow this eccentricity test, due to the poor orbital phase coverage, we can use the spuriously high radial velocity semi-amplitude to show that X-ray heating is present."850 1n order to investigate the effects of X-ray heating on the secondary stars racial velocity curve we used the mocel described by Phillips. Shahbaz Poclsiacllowski (1999).“Phe model uses a crude treatment for N-rav heating. since no satisfactory robust model exists for the elfects of external heating in stars.," In order to investigate the effects of X-ray heating on the secondary star's radial velocity curve we used the model described by Phillips, Shahbaz Podsiadlowski (1999).The model uses a crude treatment for X-ray heating, since no satisfactory robust model exists for the effects of external heating in stars."851 However. it serves to illustrate the extreme," However, it serves to illustrate the extreme"852(Suuvaev&Zeldovich1972:Birkinshaw y-paramceter.,"\citep{sunyaev1972,birkinshaw1991,carlstrom2002}."853" integral of the eas pressure along the line of sight through the cluster: Iu this expression. στ is the Thomson scattering cross section. i, is the electrou mass. ο is the speed of light. 2 is the gas pressure. aud the integration is along the Inc-ofsieht."," $y$ integral of the gas pressure along the line of sight through the cluster: In this expression, $\sigma_{\rm T}$ is the Thomson scattering cross section, $m_{e}$ is the electron mass, $c$ is the speed of light, $P_{e}$ is the gas pressure, and the integration is along the line-of-sight."854 Iutegratiug y over the solid angle Q vields the inteerated Compton parameter Y. which is proportional to the thermal euergv of the cluster (Motletal.2005:Bonamenteetal.2008.hereafter BOs).," Integrating $y$ over the solid angle $\Omega$ yields the integrated Compton parameter $Y$, which is proportional to the thermal energy of the cluster \citep[][hereafter B08]{motl2005, bonamente2008}."855. This paper reports observations of +=1 clusters made with the Suuvaev-Zeldovich Array (SZA)). aud ainis to provide coustraiuts ou the eas properties of the clusters. and a comparison to existing scaling relations.," This paper reports observations of $z\geq 1$ clusters made with the Sunyaev-Zel'dovich Array ), and aims to provide constraints on the gas properties of the clusters, and a comparison to existing scaling relations."856 Tn Section 2 we describe the sample of clusters. Section describes the collection aud analysis of the ddata. and Section { preseuts an analysis of cluster rav data (vhere available} from the aand oobservatories.," In Section \ref{sec:sample} we describe the sample of clusters, Section \ref{sec:szadata} describes the collection and analysis of the data, and Section \ref{sec:xrays} presents an analysis of cluster X-ray data (where available) from the and observatories."857 The results aud discussion. including a conrparison of SZ and X-ray cluster gas properties. are eiven in Section 5..," The results and discussion, including a comparison of SZ and X-ray cluster gas properties, are given in Section \ref{sec:results}."858 Throughout this docuueut we use the cosmiologieal parameters J/9j2773|. ο=0.27 aud O4=0.73.," Throughout this document we use the cosmological parameters 73, $\Omega_m=0.27$ and $\Omega_{\Lambda}=0.73$."859 Unless otherwise stated. all uncertainties correspond to the aud perceutiles of the probability distribution function confidence interval).," Unless otherwise stated, all uncertainties correspond to the and percentiles of the probability distribution function confidence interval)."860 We obtained oobservatious of an ad hoc sample of eleven clusters with 2 c discovered in either X-rav or infrared (IB) nuaeiue surveys basic information about the clusters, We obtained observations of an ad hoc sample of eleven clusters with $z\geq$ 1 discovered in either X-ray or infrared (IR) imaging surveys — basic information about the clusters861For inclinations close to 90°. the flux becomes roughly proportional to sin /. hence weakly sensitive to 7.,"For inclinations close to $^{\circ}$, the flux becomes roughly proportional to $\sin$ $i$, hence weakly sensitive to $i$."862 For this reason. inclinations in the 80—90° range cannot always be distinguished. and the uncertainty on the inclination increases with the inclination despite larger modulations.," For this reason, inclinations in the $80-90^{\circ}$ range cannot always be distinguished, and the uncertainty on the inclination increases with the inclination despite larger modulations."863 Although the accuracy obtained with EChO ts lower than JWST for a given number of orbits. EChO will have the possibility of dedicating more time to a given target. reducing the S/N to levels comparable to or better than those achievable with JWST. hopefully with a significantly improved stability and the capability of observing spectral phase curves over a wider spectral domain simultaneously.," Although the accuracy obtained with EChO is lower than JWST for a given number of orbits, EChO will have the possibility of dedicating more time to a given target, reducing the S/N to levels comparable to or better than those achievable with JWST, hopefully with a significantly improved stability and the capability of observing spectral phase curves over a wider spectral domain simultaneously."864 Using the 2.5—5 um domain would better characterize the hottest planets., Using the $2.5-5~\mu$ m domain would better characterize the hottest planets.865 On JWST. measurements in this window imply the use of NIRSpec. an instrument that cannot be used simultaneously with MIRI. while EChO spectrometer should cover the whole 0.5—16 um window.," On JWST, measurements in this window imply the use of NIRSpec, an instrument that cannot be used simultaneously with MIRI, while EChO spectrometer should cover the whole $0.5-16~\mu$ m window."866 The results presented in this work assume that the observation covers two orbital periods. which will certainly be required in practice to extract the periodic planetary signal from the stellar variability.," The results presented in this work assume that the observation covers two orbital periods, which will certainly be required in practice to extract the periodic planetary signal from the stellar variability."867 We tested on several cases that the error on the albedo. the inclination and the radius decreases as 1/VN. where N is the number of orbits observed.," We tested on several cases that the error on the albedo, the inclination and the radius decreases as $1/\sqrt{N}$, where $N$ is the number of orbits observed."868 Also for observations covering N orbits. the values of R. A. and i obtained for each individual orbit (or for a number of orbits smaller than N) provide an information on their dispersion.," Also for observations covering $N$ orbits, the values of $R$, $A$, and $i$ obtained for each individual orbit (or for a number of orbits smaller than $N$ ) provide an information on their dispersion."869 If we combine the projected mass Msin/ measured from radial velocity observations with the constraint on the inclination from the phase curve. we obtain an estimate of the true mass.," If we combine the projected mass $M \sin i$ measured from radial velocity observations with the constraint on the inclination from the phase curve, we obtain an estimate of the true mass."870 Retrieved mass and radius and their associated uncertainty can be compared with theoretical models to assess the composition of the planet., Retrieved mass and radius and their associated uncertainty can be compared with theoretical models to assess the composition of the planet.871 Figure 16 shows mass-radius relations of ice/rock and rock/iron planets from ? and the range of mass and radii obtained from phase curves for two planets (R=1.5Re. Msini=4M. and R=2Rs. Msini=8 Ma) around a 0.5 and a 0.8 Ma star with an orbital period of three days.," Figure \ref{masserad} shows mass-radius relations of ice/rock and rock/iron planets from \citet{Fortney2007err} and the range of mass and radii obtained from phase curves for two planets $R=1.5~R_{\oplus}$, $M\sin{i}=4~M_{\oplus}$ and $R=2~R_{\oplus}$, $M\sin{i}=8~M_{\oplus}$ ) around a 0.5 and a 0.8 $M_{\odot}$ star with an orbital period of three days."872" The planets around the 0.8 M. star logically give the best estimate of the composition,", The planets around the 0.8 $M_{\odot}$ star logically give the best estimate of the composition.873 The uncertainty on the composition is dominated by the uncertainty on the mass. and one should also include the error on the measurement of Msini itself.," The uncertainty on the composition is dominated by the uncertainty on the mass, and one should also include the error on the measurement of $M \sin{i}$ itself."874 Interestingly. the uncertainty on the planet radius does not come directly from the uncertainty on the stellar radius as 1t does when the planetary radius is inferred from the primary transit depth. in the case of transiting planets.," Interestingly, the uncertainty on the planet radius does not come directly from the uncertainty on the stellar radius as it does when the planetary radius is inferred from the primary transit depth, in the case of transiting planets."875" Indeed. the depth of the transit provides the ratio R,/R, and an estimate of A, therefore requires a value for R,. which comes with its uncertainties."," Indeed, the depth of the transit provides the ratio $R_{p}/R_{\star}$ and an estimate of $R_p$ therefore requires a value for $R_{\star}$, which comes with its uncertainties."876 When deduced from the thermal phase curve. the radius estimate ts also affected by uncertainties (for instance on the luminosity of the star or on the orbital distance). but not coming directly from the radius.," When deduced from the thermal phase curve, the radius estimate is also affected by uncertainties (for instance on the luminosity of the star or on the orbital distance), but not coming directly from the radius."877 Errors on the stellar luminosity and the stellar mass (used to convert an orbital period into an orbital distance) do. however. result in retrieval errors.," Errors on the stellar luminosity and the stellar mass (used to convert an orbital period into an orbital distance) do, however, result in retrieval errors."878 As another illustration. we show in Fig.," As another illustration, we show in Fig."879 17. the result for three known exoplanets bb. GJ581 b. and GJ581 e. see Sect. 5.2)).," \ref{MR-candidates} the result for three known exoplanets b, GJ581 b, and GJ581 e, see Sect. \ref{candidates}) ),"880 assuming that they are made of silicates (an assumption that is probably not realistic for GJ58] b. whose volatile content must be high considering its large mass).," assuming that they are made of silicates (an assumption that is probably not realistic for GJ581 b, whose volatile content must be high considering its large mass)."881 We do not know a priori whether the observed planet has an atmosphere of not., We do not know a priori whether the observed planet has an atmosphere of not.882 As shown by Selsis et al. (, As shown by Selsis et al. (8832011). the presence of an atmosphere can be inferred from the variation spectrum.,"2011), the presence of an atmosphere can be inferred from the variation spectrum."884 We did. however. test our R-A—i retrieval procedure (which assumes no atmosphere) on phase curves computed for a planet with a dense atmosphere.," We did, however, test our $R-A-i$ retrieval procedure (which assumes no atmosphere) on phase curves computed for a planet with a dense atmosphere."885 The planet is a 1.8 Re rocky planet with a 1 bar CO» atmosphere. in a [:1 spin-orbit resonance on an 8-day orbit around an M3 dwarf. with 607 inclination.," The planet is a 1.8 $_{\oplus}$ rocky planet with a 1 bar $_2$ atmosphere, in a 1:1 spin-orbit resonance on an 8-day orbit around an M3 dwarf, with $60^{\circ}$ inclination."886 The structure of the atmosphere and the associated radiative transfer has been modeled with a 3D GCM (global climate model) described in ?.., The structure of the atmosphere and the associated radiative transfer has been modeled with a 3D GCM (global climate model) described in \citet{Selsis2011}.887" Our model obviously fails to fit the phase curves variations at all wavelengths. which by itself shows that the ""no atmosphere"" assumption is wrong."," Our model obviously fails to fit the phase curves variations at all wavelengths, which by itself shows that the “no atmosphere” assumption is wrong."888 If we treat each spectral band independently of the others. our model can obtain a set of R. A. and i with reasonable y at some wavelengths but the retrieved. values strongly vary from one wavelength to another.," If we treat each spectral band independently of the others, our model can obtain a set of $R$, $A$, and $i$ with reasonable $\chi^2$ at some wavelengths but the retrieved values strongly vary from one wavelength to another."889 Figure 18. shows the retrieved values as a function of wavelength (no noise is considered in this retrieval)., Figure \ref{specatmo1} shows the retrieved values as a function of wavelength (no noise is considered in this retrieval).890 As in the variation spectrum deseribed by Selsis et al. (?)..," As in the variation spectrum described by Selsis et al. \citeyearpar{Selsis2011},"891" the signatures of molecular absorption can be seen in these plots. in particular the 2.7. 4.3. and 15 ym bands of CO» in the “inclination spectrum""."," the signatures of molecular absorption can be seen in these plots, in particular the 2.7, 4.3, and 15 $\mu$ m bands of $_2$ in the “inclination spectrum”."892 This is because different wavelengths probe different altitudes in the atmospheres. with different day-night temperature contrasts.," This is because different wavelengths probe different altitudes in the atmospheres, with different day-night temperature contrasts."893 In absorption bands. the flux comes from high altitudes with smooth day-night contrast. while in atmospheric windows. the flux comes from the surface that exhibits a temperature distribution that differs less from the airless case.," In absorption bands, the flux comes from high altitudes with smooth day-night contrast, while in atmospheric windows, the flux comes from the surface that exhibits a temperature distribution that differs less from the airless case."894 As an example. we show in Fig.," As an example, we show in Fig."895 19 the results of the fit for three wavelengths., \ref{atmo} the results of the fit for three wavelengths.896 We only fit the variations and not the absolute flux. which i$ why the solution found by our procedure can produce a phase curve that is shifted vertically.," We only fit the variations and not the absolute flux, which is why the solution found by our procedure can produce a phase curve that is shifted vertically."897 Because we only consider synchronized. planets. which ts equivalent to a planet with no thermal inertia. our modeled phase curves cannot exhibit the phase shift that atmospheric circulation can produce.," Because we only consider synchronized planets, which is equivalent to a planet with no thermal inertia, our modeled phase curves cannot exhibit the phase shift that atmospheric circulation can produce."898 If we no longer consider synchronized planets and let the rotation rate and the thermal inertia be free parameters. our airless model may fit a monochromatic phase curve obtained with an atmosphere with better agreement. by reproducing the phase shift.," If we no longer consider synchronized planets and let the rotation rate and the thermal inertia be free parameters, our airless model may fit a monochromatic phase curve obtained with an atmosphere with better agreement, by reproducing the phase shift."899 In this case. the displacement of the hot spot (compared with the exact substellar location) ts due not to horizontal circulation. as in an atmosphere. but to vertical heat diffusion.," In this case, the displacement of the hot spot (compared with the exact substellar location) is due not to horizontal circulation, as in an atmosphere, but to vertical heat diffusion."900 However. retrieved rotation rate and thermal inertia would also depend on the wavelength. as for the inclination. radius. and albedo.," However, retrieved rotation rate and thermal inertia would also depend on the wavelength, as for the inclination, radius, and albedo."901 Also. for planets hot enough to produce an observable infrared phase curve. on cireular orbits. synchronization occurs on extremely short timescales so there," Also, for planets hot enough to produce an observable infrared phase curve, on circular orbits, synchronization occurs on extremely short timescales so there"902"possibly unphysical outlier estimated mass exceeds those of other fragments of (itssimilar size by a factor 2, possibly because of neglected protostellar heating).","possibly unphysical outlier (its estimated mass exceeds those of other fragments of similar size by a factor 2, possibly because of neglected protostellar heating)."903 The limiting law is derived by searching for the smallest intercept for which mo(r/pc) does still provide an upper limit to the data.," The limiting law is derived by searching for the smallest intercept for which $m_0 \, (r / {\rm pc})^b$ does still provide an upper limit to the data."904" Practically, this is done by varying b until max[m(r)/(r/pc)""] is Interestingly, our sample clouds with massive star formation exceed the limiting relation refeq:mass-referencejimit moremassivemass))"," Practically, this is done by varying $b$ until $\max[m(r) / (r / {\rm pc})^b]$ is Interestingly, our sample clouds with massive star formation exceed the limiting relation \\ref{eq:mass-reference_limit-low-mass}) )."905.ThisisshowninFig.reffig:mass—size comparison((b)., This is shown in \\ref{fig:mass-size-comparison}( (b).906FortheOrion AcloudeinéG fittest dag.a{G}) radius range.," For the Orion A cloud and G10, we derive an excess of up to a factor 10 in the $0.01 \lesssim r / {\rm pc} \lesssim 2$ radius range."907 This suggests that these clouds have a structure significantly different from what is found for clouds not containing such stars , This suggests that these clouds have a structure significantly different from what is found for clouds not containing such stars \\ref{fig:mass-size-comparison}[ [a]).908"In this light, ((6)) reffig:mass-size-comparison[[a]).may approximate a limit for massive star formation: it could be that only clouds also containing fragments that exceed ((6)) are able to form massive stars."," In this light, \ref{eq:mass-reference_limit-low-mass}) ) may approximate a limit for massive star formation: it could be that only clouds also containing fragments that exceed \ref{eq:mass-reference_limit-low-mass}) ) are able to form massive stars."909 Larger samples of clouds forming massive stars must be screened to prove this point., Larger samples of clouds forming massive stars must be screened to prove this point.910" Note, however, that most fragments in Orion A do fulfill ((6))."," Note, however, that most fragments in Orion A do fulfill \ref{eq:mass-reference_limit-low-mass}) )."911 This cloud does therefore also contain objects that have masses and sizes not distinguishable from those found for clouds not forming massive stars., This cloud does therefore also contain objects that have masses and sizes not distinguishable from those found for clouds not forming massive stars.912" As a mass-size limit for clouds not forming massive stars, ((6)) is probably uncertain to just a few10%."," As a mass-size limit for clouds not forming massive stars, \ref{eq:mass-reference_limit-low-mass}) ) is probably uncertain to just a few."913". If we, e.g., not use Ophiuchus data in the derivation of ((6)), then Ophiuchus would exceed the resulting mass-size limit by30%."," If we, e.g., not use Ophiuchus data in the derivation of \ref{eq:mass-reference_limit-low-mass}) ), then Ophiuchus would exceed the resulting mass-size limit by."914". If we do the same with Perseus data, the excess is15%.."," If we do the same with Perseus data, the excess is."915 It is plausible to expect similar changes for other regions not forming massive stars., It is plausible to expect similar changes for other regions not forming massive stars.916" Observational uncertainties are most likely of a similar order, if one adopts the mass measurement techniques used here (i.e., dust emission and extinction)."," Observational uncertainties are most likely of a similar order, if one adopts the mass measurement techniques used here (i.e., dust emission and extinction)."917" Then, several uncertainties (e.g., dust opacities) are simply removed by calibration to the same standard."," Then, several uncertainties (e.g., dust opacities) are simply removed by calibration to the same standard."918" In an absolute sense (i.e., when considering the true masses), ((6)) is as accurate as the mass conversion standards used here (e.g., relation of dust emission and mass)."," In an absolute sense (i.e., when considering the true masses), \ref{eq:mass-reference_limit-low-mass}) ) is as accurate as the mass conversion standards used here (e.g., relation of dust emission and mass)."919 These are probably uncertain to less than a factor 2., These are probably uncertain to less than a factor 2.920" We stress that, excluding observational uncertainties, ((6)) provides a strict upper mass limit to the solar neighborhood samplehere."," We stress that, excluding observational uncertainties, \ref{eq:mass-reference_limit-low-mass}) ) provides a strict upper mass limit to the solar neighborhood sample."921. Clouds violating ((6)) are not similar to the clouds in the solar neighborhood sample discussed here., Clouds violating \ref{eq:mass-reference_limit-low-mass}) ) are not similar to the clouds in the solar neighborhood sample discussed here.922 This statement is sufficient for many purposes., This statement is sufficient for many purposes.923 Inspection of reffig:cloud-sample and 2 suggests that all solar neighborhood clouds have similar masses at given size for radii =1pc., Inspection of \\ref{fig:cloud-sample} and \ref{fig:mass-size-comparison} suggests that all solar neighborhood clouds have similar masses at given size for radii $\gtrsim 1 ~ \rm pc$.924" Specifically, the most massive fragments at given radius are essentially all within +30% of in the 1€r/pc4 radius range, when considering 'Taurus, Ophiuchus, Perseus, and the Pipe Nebula."," Specifically, the most massive fragments at given radius are essentially all within $\pm 30\%$ of in the $1 \le r / {\rm pc} \le 4$ radius range, when considering Taurus, Ophiuchus, Perseus, and the Pipe Nebula."925" Also our preliminary Orion A data is, at 11pc radius, within of this law—with the caveat that we cannot examine whether Orion A follows ((7)) down to —1pc radius."," Also our preliminary Orion A data is, at $11 ~ \rm pc$ radius, within of this law—with the caveat that we cannot examine whether Orion A follows \ref{eq:mass-reference_large-radii}) ) down to $\sim 1 ~ \rm pc$ radius."926 It thus appears that—with Orion A as a possible exception—all local clouds are similar in their large-scale mass structure., It thus appears that—with Orion A as a possible exception—all local clouds are similar in their large-scale mass structure.927" This mass-size relation is very similar to the one originally derived by ?,, m(r)=460Ma(r/pc)!? (see refeq:mass-size-larson above)."," This mass-size relation is very similar to the one originally derived by \citet{larson1981:linewidth_size}, $m(r) = 460 \, M_{\sun} \, (r / {\rm pc})^{1.9}$ (see \\ref{eq:mass-size-larson} above)."928" Our study thus confirms his result—but only for spatial scales Z,1pc.", Our study thus confirms his result—but only for spatial scales $\gtrsim 1 ~ \rm pc$.929" As we show throughout this paper and reffig:global-slopes,f and5)), (e.g., nosinglemass[6]]− sizerelationdescribesallstructuralaspectsof ourobservationaldata."," As we show throughout this paper (e.g., ] and \\ref{fig:global-slopes_sf} and \ref{fig:slope-comparison}) ), no single mass-size relation describes all structural aspects of our observational data."930" Some cloud fragments 1pc are, however, much than solar neighborhoodZ clouds of similar Obl"," Some cloud fragments $\gtrsim 1 ~ \rm pc$ are, however, much more massive than solar neighborhood clouds of similar size."931 an order of magnitude.tether The exeanplec," G10, for example, violates \ref{eq:mass-reference_large-radii}) ) by about an order of magnitude."932esiolsimilarity between local Oógthb0300clouds, The similarity between local clouds933the z ~ 1 stacked points are only considered as lower limits and we were not able to stack z ~ 2 LBGs.,the z $\sim$ 1 stacked points are only considered as lower limits and we were not able to stack z $\sim$ 2 LBGs.934" To understand the origin of this effect, we build a simple closed box model (see Pageletal. 1997)), assuming several exponentially decreasing star formation histories Ψ(4)=Woe-*/7, with 7 = 0.1, 1 and GGyr."," To understand the origin of this effect, we build a simple closed box model (see \citealt{pagel97}) ), assuming several exponentially decreasing star formation histories $\Psi(t) = \Psi_0 e^{-t/\tau}$, with $\tau$ = 0.1, 1 and Gyr."935" We assume a mass of cold gas that forms stars following a Salpeter initial mass Mg4,function, and thus produce heavy elements."," We assume a mass of cold gas $M_{\rm gas}$ that forms stars following a Salpeter initial mass function, and thus produce heavy elements."936" Mg, evolves as follows:", $M_{\rm gas}$ evolves as follows:937barvon/stellar mass fraction f..,baryon/stellar mass fraction $f_*$.938" The NEW prolile (Navarro.Frenk&White1996) used to model the initial dark matter halo is defined by where (he scale length ry is related to the virial radius by e=μενκ. c). and Aly,=(1—f,LM, is the mass in dark matter."," The NFW profile \citep{nfw96} used to model the initial dark matter halo is defined by where the scale length $r_s$ is related to the virial radius by $c = r_{vir}/r_s$, $f(c) = \ln(1+c) - c/(1+c)$ , and $M_{dm} = (1-f_*)M_{vir}$ is the mass in dark matter."939 The average concentration was modeled by and the individual halos have a log-normal dispersion in their concentrations of (base 10) around the average (Bullocketal.2001)., The average concentration was modeled by and the individual halos have a log-normal dispersion in their concentrations of $\sigma_c = 0.18$ (base 10) around the average \citep{bullock01}.940. These initial models neglect the compression of the dark matter densitv profile by the more concentrated. barvons., These initial models neglect the compression of the dark matter density profile by the more concentrated baryons.941 We estimated the changes in the dark matter distribution using (he adiabatic compression model of Bhunenthaletal.(1986)., We estimated the changes in the dark matter distribution using the adiabatic compression model of \citet{blumenthal86}.942. This approximation max exaggerate the compression etal. 2004).. so we should regard our compressed ancl uncompressed results as bouncing the possible effects of adiabatic compression.," This approximation may exaggerate the compression \citep{gnedin04}, so we should regard our compressed and uncompressed results as bounding the possible effects of adiabatic compression."943 The observations provide (wo constraints. (he mass inside the Einstein radius. and the stellar velocity dispersion.," The observations provide two constraints, the mass inside the Einstein radius, and the stellar velocity dispersion."944" For any value of ο and f;. we use the projected mass inside the Einstein radius to determine M,;, (which also determines r,;,). then use the spherical Jeans equation and a constant orbital isotropy ο (o compute (he velocity dispersion expected for the measurement aperture."," For any value of $c$ and $f_*$ , we use the projected mass inside the Einstein radius to determine $M_{vir}$ (which also determines $r_{vir}$ ), then use the spherical Jeans equation and a constant orbital isotropy $\beta$ to compute the velocity dispersion expected for the measurement aperture."945 The effects of seeing were modeled using a Gaussian PSF with the observed EFWIIM of the observations., The effects of seeing were modeled using a Gaussian PSF with the observed FWHM of the observations.946" Given the estimated dispersion 6;,,4,,4,4. the measured dispersion o; ancl its uncertainties ¢,; for galaxy 7. we estümale a goodness of lit.. \σι)>P=σι!—0i)/fe; "," Given the estimated dispersion $\sigma_{i,model}$, the measured dispersion $\sigma_i$ and its uncertainties $e_{\sigma i}$ for galaxy $i$ , we estimate a goodness of fit ${\chi_i}^2(\sigma_i)=(\sigma_{i,model}-\sigma_i)^2/e_{\sigma i}^2$."947"We- model the mass-to-lightB ratiosB ofH the stars usingB the standard power law (e.g. vanDokkunm&Frans1996:Treu2001:Koopmansetal. 2006). where (M./L), is the value today aud dlogCM,/L)/dz is the rate al which it changes with redshift z."," We model the mass-to-light ratios of the stars using the standard power law (e.g. \citealt{vanf96,treu01,rk05,ktbbm06}) ), where $({M_{\ast} / L})_0$ is the value today and ${d \log(M_{\ast}/L)/ d z}$ is the rate at which it changes with redshift $z$."948 This in turn defines a goodness of fit N2CCM/L);) with which the model fits the logarithm of the mass-to-lisht ratio (U/L); of galaxy 7. defined by the ratio of the estimated stellar mass (a model parameter)to the observed Iuminositv. given i(s uncertainties AL;/(n(10)L;).," This in turn defines a goodness of fit $\chi_i^2((M/L)_i)$ with which the model fits the logarithm of the mass-to-light ratio $(M/L)_i$ of galaxy $i$, defined by the ratio of the estimated stellar mass (a model parameter)to the observed luminosity, given its uncertainties $e_{Li}=\Delta(\log(M/L)_i= \Delta L_i/(\ln(10)L_i)$ ."949" These two terms define a probability of fitting the velocity dispersion P(o;|£)=exp(—2(0;)/2)/v2xe,; and the mass-to-lightratio", These two terms define a probability of fitting the velocity dispersion $P(\sigma_i|\bfxi) = \exp(-\chi_i^2(\sigma_i)/2)/\sqrt{2\pi}e_{\sigma i}$ and the mass-to-lightratio950extracted by mulliplexine (he signal over a range of wavelengths. rather than relvine on measurements made within narrow wavelength intervals. such as line index measurements.,"extracted by multiplexing the signal over a range of wavelengths, rather than relying on measurements made within narrow wavelength intervals, such as line index measurements."951 A basic piece of information that can be extracted. are the spectral tvpes of the resolved stars., A basic piece of information that can be extracted are the spectral types of the resolved stars.952 This is relevant for stellar content studies because spectralivpe can serve as a proxy for color. allowing comparisons to be made with photometric observations al larger radii.," This is relevant for stellar content studies because spectral-type can serve as a proxy for color, allowing comparisons to be made with photometric observations at larger radii."953 Spectral (vpes were determined by cross-correlating the. M32. spectra with those of relerence stars [rom Rayner. Cushing. Vacca (2009). which were downloaded [rom the IRTF website.," 	Spectral types were determined by cross-correlating the M32 spectra with those of reference stars from Rayner, Cushing, Vacca (2009), which were downloaded from the IRTF website."954 The IRTF spectra were re-sampled and smoothed to match the wavelength saanpling and spectral resolution of the processed NIES spectra., The IRTF spectra were re-sampled and smoothed to match the wavelength sampling and spectral resolution of the processed NIFS spectra.955 The height of the central peak in the cross-correlation function measures the degree of similarity between the (wo spectra., The height of the central peak in the cross-correlation function measures the degree of similarity between the two spectra.956" The amplitude of the cross-correlation peak can be biased by a single strong leature. such as the ""CO (2.0) band head."," The amplitude of the cross-correlation peak can be biased by a single strong feature, such as the $^{12}$ CO (2,0) band head."957" Therefore. in addition to correlations in the 2.1—2.3/n wavelength inlerval. a second set of correlations was done in the 2.1—2.28j0n interval to avoid the ""CO band head and thereby base the spectral matching on the strengths of atomic and less prominent molecular features."," Therefore, in addition to correlations in the $2.1 - 2.3\mu$ m wavelength interval, a second set of correlations was done in the $2.1 - 2.28\mu$ m interval to avoid the $^{12}$ CO band head and thereby base the spectral matching on the strengths of atomic and less prominent molecular features."958 Significantly. (he cross-correlations involving the wavelength intervals with and without the PCO band head produced consistent results. indicating (hat the spectral typing is not biased by a single strong feature.," Significantly, the cross-correlations involving the wavelength intervals with and without the $^{12}$ CO band head produced consistent results, indicating that the spectral typing is not biased by a single strong feature."959 The highest degree of semblance resulted when (he spectra in Figure 2 were compared with (he MSI star., 	The highest degree of semblance resulted when the spectra in Figure 2 were compared with the M5III star.960 The next best fit was lor M61ILII. while (the peaks of the cross-correlation funelions involving (vpes MOIII and C2.2 were substantially lower (han those involving MO Il] - MG III stars.," The next best fit was for M6III, while the peaks of the cross-correlation functions involving types M9III and C2.2 were substantially lower than those involving M0 III - M6 III stars."961 The degree of similarity between (he near-intrarecl spectra of the M32 sources and the Galactic M5 III standard star is demonstrated in Figure 4. where the mean spectrum of sources 1. 3. and 8 is compared with that of selected stars from Rayner et al. (," The degree of similarity between the near-infrared spectra of the M32 sources and the Galactic M5 III standard star is demonstrated in Figure 4, where the mean spectrum of sources 1, 3, and 8 is compared with that of selected stars from Rayner et al. ("9622009).,2009).963 The PCO (2.0) band head and the lines of Na LI. Fe L and Ca I in the mean M32 spectrum are similar in strength to those in the M5 III spectrum.," The $^{12}$ CO (2,0) band head and the lines of Na I, Fe I, and Ca I in the mean M32 spectrum are similar in strength to those in the M5 III spectrum."964 The similarity in spectral-(wpes is significant. as it indicates that (he upper regions ol the AGB in M32 are populated by stars with a narrow range in effective temperature.," 	The similarity in spectral-types is significant, as it indicates that the upper regions of the AGB in M32 are populated by stars with a narrow range in effective temperature."965 Adopting the relation between spectral tvpe and J—A from Bessell Brett (1983) for solar neighborhood giants. (hen these sources have JJ—A=1.21.3. which is consistent with the color of the upper AGB at larger radii in M32 (Davidge Jensen 2007).," Adopting the relation between spectral type and $J-K$ from Bessell Brett (1988) for solar neighborhood giants, then these sources have $J-K = 1.2 - 1.3$, which is consistent with the color of the upper AGB at larger radii in M32 (Davidge Jensen 2007)."966 The amplitude of the cross-correlation function also contains information about the strengths of absorption features. albeit multiplexed over a range of elements.," 	The amplitude of the cross-correlation function also contains information about the strengths of absorption features, albeit multiplexed over a range of elements."967 Davidge οἱ al. (, Davidge et al. (9682008) found that the integrated spectrum of M32 [alls near relations defined by solar neighborhood stars on the (Ca I. CO) and (Na LI. CO) diagrams. suggesting that stars in M32 formed from material (hat experienced slow enrichment: hence. the use of solar neighborhood reference stus for abundance analysis is appropriate.,"2008) found that the integrated spectrum of M32 falls near relations defined by solar neighborhood stars on the (Ca I, $^{12}$ CO) and (Na I, $^{12}$ CO) diagrams, suggesting that stars in M32 formed from material that experienced slow enrichment; hence, the use of solar neighborhood reference stars for abundance analysis is appropriate."969 The dominant features, The dominant features970wilh the data accumulated after the [ist three vears of operation.,with the data accumulated after the first three years of operation.971 Now alter six vears of data have been accumulated. Milagro has reached a sensitivity. equal to about 20 per cent of the Crab flux at 20 TeV median energv aud should be able to detect 341 sources., Now after six years of data have been accumulated Milagro has reached a sensitivity equal to about 20 per cent of the Crab flux at 20 TeV median energy and should be able to detect $3\pm1$ sources.972 The Milagro Collaboration has recently published the survey of the Northern sky in (he region between 30°«/220° and —10*<b<10° at à threshold of 20 TeV and a threshold sensitivity of about 20 percent of the Crab detecting 4 sources Abdoetal.(2007)., The Milagro Collaboration has recently published the survey of the Northern sky in the region between ${30}^{o}<l<{220}^{o}$ and ${-10}^{o}<b<{10}^{o}$ at a threshold of 20 TeV and a threshold sensitivity of about 20 percent of the Crab detecting 4 sources \cite{Abdo:2007}.973. The number of sources detected is in agreement with our predictions., The number of sources detected is in agreement with our predictions.974" Alter only one vear of operation the proposed experiment ILAWC will have surveved the region of the sky with longitude 5°</«110° and 130°</«250° and latitude —10""<510° at 30mCrab sensitivitv above 1 TeV and should have detected 19x5 IIESS-like SNRs and PWNe.", After only one year of operation the proposed experiment HAWC will have surveyed the region of the sky with longitude ${5}^{o}<l<{110}^{o}$ and ${130}^{o}<l<{250}^{o}$ and latitude ${-10}^{o}<b<{10}^{o}$ at 30mCrab sensitivity above 1 TeV and should have detected $19\pm5$ HESS-like SNRs and PWNe.975 The predictions given here for Milagro and ILAWC are valid unless the source spectra steepen or cut-olf below the Milagro threshold., The predictions given here for Milagro and HAWC are valid unless the source spectra steepen or cut-off below the Milagro threshold.976 Ilowever. for the sources detected by LESS the spectrum is predominantly well characterized by a single power law.," However, for the sources detected by HESS the spectrum is predominantly well characterized by a single power law."977 Thanks to the logN-logsS relation we obtained a lower limit for the contribution of unresolved IIESS-like sources to the diffuse emission measured by Milagro., Thanks to the logN-logS relation we obtained a lower limit for the contribution of unresolved HESS-like sources to the diffuse emission measured by Milagro.978 Here we will asstune that the density of VITE 5-rav. source candidates. SNRs and PWNe. follows the volume density of SNRs or of pulsars in the Galactic Plane as observed αἱ radio wavelengths and (heir luminosity function is a power law. and we will (hen estimate their contribution to the Milagro diffuse emission.," Here we will assume that the density of VHE $\gamma$ -ray source candidates, SNRs and PWNe, follows the volume density of SNRs or of pulsars in the Galactic Plane as observed at radio wavelengths and their luminosity function is a power law, and we will then estimate their contribution to the Milagro diffuse emission."979 since the data on HESS sources are (oo sparse lo constrain their luminosity fanction. we will leave it as a parametrised input.," Since the data on HESS sources are too sparse to constrain their luminosity function, we will leave it as a parametrised input."980 The Iuminositv function @(£) will be a power law with different indices à. varving between -1 and -2 The assumed luminosity [function will then be compared with the HESS source counts to fix the normalisation c., The luminosity function $\Phi(L)$ will be a power law with different indices $\alpha$ varying between -1 and -2 The assumed luminosity function will then be compared with the HESS source counts to fix the normalisation $c$.981" In Eq.(12)) £.,=1x10*erg/s.", In \ref{eqn:luminosity}) ) ${L_{\gamma}}_0= 1 \times {10}^{34} erg/s$.982 The range in luminosities for the IIESS sources. lor which the distance and thus the luminosity is known. varies between LOerg/s and 10erg/s.," The range in luminosities for the HESS sources, for which the distance and thus the luminosity is known, varies between ${10}^{31} erg/s$ and ${10}^{36} erg/s$."983 In fact. most sources of 5-rav in the Galaxy are located close to the plane of the Galaxy. within a region which extends trom δν=0.3 kpe up to Ding.=30 kpe (Swordy2003).," In fact, most sources of $\gamma$ -ray in the Galaxy are located close to the plane of the Galaxy, within a region which extends from $D_{min}=0.3$ kpc up to $D_{max}=30$ kpc \citep{Swordy}."984. The range in luminosity for the HESS sample can then be found from the LESS sensitivity (we assume 6 percent of (he Crab flux) and the maximum {his detected, The range in luminosity for the HESS sample can then be found from the HESS sensitivity (we assume 6 percent of the Crab flux) and the maximum flux detected985The Sloan Digital Sky Survey obtains spectra from a variety of objects based on various color and magnitude selection cuts (Stoughtonοἱal...2002).,The Sloan Digital Sky Survey obtains spectra from a variety of objects based on various color and magnitude selection cuts \citep{stoughton02}.986". The survey is not complete in most of the star categories. as a limited number of fibers (640) are used in each of the SDSS fields. and stellar targets are assigned only after the primary categories (QSOs, galaxies)."," The survey is not complete in most of the star categories, as a limited number of fibers (640) are used in each of the SDSS fields, and stellar targets are assigned only after the primary categories (QSOs, galaxies)."987 The spectra cover the full wwavelength range. which includes the main molecular features used to identify cool dwarfs and subdwarfs.," The spectra cover the full wavelength range, which includes the main molecular features used to identify cool dwarfs and subdwarfs."988 The SDSS second data release (DR2) listed 13.379 spectra of sources identified as cool and ultra-cool stars (spectral subtype M and later).," The SDSS second data release (DR2) listed 13,379 spectra of sources identified as cool and ultra-cool stars (spectral subtype M and later)."989 The DR2 covered a total survey area of 2627 square degrees or a little over of the sky., The DR2 covered a total survey area of 2627 square degrees or a little over of the sky.990 In an attempt to detect ultra-cool L subdwarfs from this sample. we have systematically examined the spectra form all stellar sources with very red optical-to-infrared color.," In an attempt to detect ultra-cool L subdwarfs from this sample, we have systematically examined the spectra form all stellar sources with very red optical-to-infrared color."991 First. we identified all possible counterparts to the 13.379 late-type stars in the 2MASS All-Sky catalog of point source (2MASS.Cutrierαἱ.2003).," First, we identified all possible counterparts to the 13,379 late-type stars in the 2MASS All-Sky catalog of point source \citep{Cetal03}."992". Then we assembled spectra of all the stars with magnitude 7—18 and color (r—K,)76.0. which eliminating from the sample most objects with spectral subtypes M6 or earlier."," Then we assembled spectra of all the stars with magnitude $r>$ 18 and color $(r-K_{s})>$ 6.0, which eliminating from the sample most objects with spectral subtypes M6 or earlier."993 We visually inspected all the spectra in search of any star with a peculiar spectral energy distribution., We visually inspected all the spectra in search of any star with a peculiar spectral energy distribution.994 All spectra were found to be consistent with either late-type M dwarfs or L dwarfs. except for only one which clearly stood out from the group: the spectrum of the star125637—-0224.," All spectra were found to be consistent with either late-type M dwarfs or L dwarfs, except for only one which clearly stood out from the group: the spectrum of the star."995. Sloan photometry shows 125637—0224to be very faint 1n the optical. but it has relatively bright counterparts in both the 2MASS and DENIS infrared catalogs: the object is clearly very red.," Sloan photometry shows to be very faint in the optical, but it has relatively bright counterparts in both the 2MASS and DENIS infrared catalogs; the object is clearly very red."996 It is undetected in the Digital Sky Survey blue (11141) and red plates (HaF). but has a counterpart on the infrared (IVn) plates -— and is thus registered in the SuperCOSMOS Sky Archive (SSA).," It is undetected in the Digital Sky Survey blue (IIIaJ) and red plates (IIIaF), but has a counterpart on the infrared (IVn) plates – and is thus registered in the SuperCOSMOS Sky Archive (SSA)."997 Data on this unusual object are recorded in Table 1., Data on this unusual object are recorded in Table 1.998 The very red spectrum of is displayed in Figure |., The very red spectrum of is displayed in Figure 1.999 The star shows many spectral features typical of late-M and L dwarfs. which confirms that it is a very cool object and not a background star affected by reddening.," The star shows many spectral features typical of late-M and L dwarfs, which confirms that it is a very cool object and not a background star affected by reddening."1000 The dominant feature is a deep K I doublet at7700A.. with strong pressure broadened wings. similar to what is observed in mid-type L dwarfs (Kirkpatricketal.1999;Geballe2002).," The dominant feature is a deep K I doublet at, with strong pressure broadened wings, similar to what is observed in mid-type L dwarfs \citep{kirk1999,geballe2002}."1001. The spectrum also displays strong bands of CrH and FeH at aand atomic lines of RbI. all typically observed in L dwarts.," The spectrum also displays strong bands of CrH and FeH at and atomic lines of RbI, all typically observed in L dwarfs."1002 Paradoxically. also displays well-defined bands of CaH and TiO around7050A.. which are usually observed in M dwarfs and are normally absent in subtypes later than M9. due to the condensation of oxides into dust grains.," Paradoxically, also displays well-defined bands of CaH and TiO around, which are usually observed in M dwarfs and are normally absent in subtypes later than M9, due to the condensation of oxides into dust grains."1003 Indeed redward of tthe spectrum ts strongly reminiscent of a late-type M dwarf., Indeed redward of the spectrum is strongly reminiscent of a late-type M dwarf.1004" Overall. thespectrum does not fit within the standard M/L dwarf classification scheme (Kirkpatricketal.1999,2000).. and appears to be a hybrid of M-type and L-type spectral features."," Overall, thespectrum does not fit within the standard M/L dwarf classification scheme \citep{kirk1999,kirk2000}, and appears to be a hybrid of M-type and L-type spectral features."1005" However. the spectrum is strikingly similar to the optical spectrum of the ""κα star 2MASS 162643925 (Gizis&Harvin2006;Burgasseretal. 2007).. with prominent bands of TIO and CaH redward of iin what looks in all other respect like an L dwarf."," However, the spectrum is strikingly similar to the optical spectrum of the “sdL” star 2MASS 1626+3925 \citep{gizis2006,burgasser2007}, with prominent bands of TiO and CaH redward of in what looks in all other respect like an L dwarf."1006 The lingering presence of TiO bands in those ultra-cool objects is interpreted as the signature of à metal-poor atmosphere 11 which dust formation is inefficient. and which maintains metal oxides in gaseous form even at very low temperature.," The lingering presence of TiO bands in those ultra-cool objects is interpreted as the signature of a metal-poor atmosphere in which dust formation is inefficient, and which maintains metal oxides in gaseous form even at very low temperature."1007 In any case. is too cool to be classifiec an M subdwarf.," In any case, is too cool to be classified an M subdwarf."1008 With ο5)=4.15. 125637-0224ts significantly. redder 1n. the optical than the coolest know M subdwarfs (Lépine2008).," With $(r-z)=4.15$, is significantly redder in the optical than the coolest known M subdwarfs \citep{LeSc2008}."1009. But again paradoxically. the optical-to-infrared colors are significantly bluer than in field L dwarfs. and the (—7)23.31 1s more in line with subtype M6-M7 (Hawleyetal.2002).," But again paradoxically, the optical-to-infrared colors are significantly bluer than in field L dwarfs, and the $(i-J)=3.31$ is more in line with subtype M6-M7 \citep{hawley2002}."1010". Furthermore. the infrared colors of are unusual: with (J—K,) 20.606. 125637—02241s significantly bluer that any knowt field L dwarfs. which all have (/—K,)>1.0 (Hawleyet 2002)."," Furthermore, the infrared colors of are unusual: with $(J-K_{s}) = $ 0.66, is significantly bluer that any known field L dwarfs, which all have $(J-K_{s})>1.0$ \citep{hawley2002}."1011" The same blue (J—K,) color is observed in the L subdwarf 2MASS 0532482 (Burgasseretal. 2003).. which further suggest they are of a similar class."," The same blue $(J-K_{s})$ color is observed in the L subdwarf 2MASS 0532+82 \citep{burgasser2003a}, , which further suggest they are of a similar class."1012 In 2MASS 0532482, In 2MASS $+$ 821013"Subuminous B stars (sdBs) are core helitum-burning stars with very thin hydrogen envelopes and masses around 0.5M,. (Heber 1986)).","Subuminous B stars (sdBs) are core helium-burning stars with very thin hydrogen envelopes and masses around $0.5\,{\rm M_{\odot}}$ (Heber \cite{heber86}) )."1014 A large fraction of the sdB stars are members of short period binaries (Maxted et al. 20011:, A large fraction of the sdB stars are members of short period binaries (Maxted et al. \cite{maxted01};1015 Naprwotzki et al. 2004a))., Napiwotzki et al. \cite{napiwotzki04a}) ).1016 After the discovery of close binary subdwarfs. several studies aimed at determining the fraction of hot subdwarfs residing in such systems.," After the discovery of close binary subdwarfs, several studies aimed at determining the fraction of hot subdwarfs residing in such systems."1017 Samples of hot subdwarfs have been checked for radial velocity (RV) variations., Samples of hot subdwarfs have been checked for radial velocity (RV) variations.1018 The binary fraction has been determined to range from 39% to 789c (e.g. Maxted et al. 2001::," The binary fraction has been determined to range from $39\,\%$ to $78\,\%$ (e.g. Maxted et al. \cite{maxted01};"1019 Naprwotzki et al. 2004a))., Napiwotzki et al. \cite{napiwotzki04a}) ).1020 Several studies were undertaken to determine the orbital parameters of subdwarf binaries (e.g. Edelmann et al. 2005::, Several studies were undertaken to determine the orbital parameters of subdwarf binaries (e.g. Edelmann et al. \cite{edelmann05};1021 Morales-Rueda et al. 2003a))., Morales-Rueda et al. \cite{morales03a}) ).1022 The orbital periods range from 0.07 to >10d with a peak at 0.5—1.0d.," The orbital periods range from $0.07$ to $>10\,{\rm d}$ with a peak at $0.5-1.0\,{\rm d}$."1023 For close binary sdBs common envelope ejection is the most probable formation channel (Han et al. 2002. 2003)).," For close binary sdBs common envelope ejection is the most probable formation channel (Han et al. \cite{han02,han03}) )."1024 In this scenario two main sequence stars of different masses evolve in a binary system., In this scenario two main sequence stars of different masses evolve in a binary system.1025 The more massive one will reach the red giant phase first and fill its Roche lobe near the tip of the red-giant branch., The more massive one will reach the red giant phase first and fill its Roche lobe near the tip of the red-giant branch.1026 If the mass transfer to the companion is dynamically unstable. a common envelope is formed.," If the mass transfer to the companion is dynamically unstable, a common envelope is formed."1027 Due to friction the two stellar cores lose orbital energy. which ts deposited within the envelope and leads to a shortening of the binary period.," Due to friction the two stellar cores lose orbital energy, which is deposited within the envelope and leads to a shortening of the binary period."1028 Eventually the common envelope ts ejected and a close binary system is formed. which contains a core helium-burning sdB and a main sequence companion.," Eventually the common envelope is ejected and a close binary system is formed, which contains a core helium-burning sdB and a main sequence companion."1029 A binary consisting of a main sequence star and a white dwarf may evolve to a close binary sdB with a white dwarf companion Ἡ a similar way., A binary consisting of a main sequence star and a white dwarf may evolve to a close binary sdB with a white dwarf companion in a similar way.1030 Only in very special and hence rare cases tight constraints can be put on the nature of the companions. that is if the systems are eclipsing or show other indicative features 11 their light curves (see the catalogue of Ritter Kolb 2009 anc references therein).," Only in very special and hence rare cases tight constraints can be put on the nature of the companions, that is if the systems are eclipsing or show other indicative features in their light curves (see the catalogue of Ritter Kolb \cite{ritter03} and references therein)."1031 Subdwarf binaries with massive WD companions turned out to be candidates for SN [a progenitors because these systems lose angular momentum due to the emission of gravitational waves and start mass transfer., Subdwarf binaries with massive WD companions turned out to be candidates for SN Ia progenitors because these systems lose angular momentum due to the emission of gravitational waves and start mass transfer.1032 The mass transfer. or the subsequent merger of the system. may cause the WD to approach the Chandrasekhar limit. ignite carbon under degenerate conditions and explode as à SN Ia (Webbink 1984:; Iben Tutukov 1984)).," The mass transfer, or the subsequent merger of the system, may cause the WD to approach the Chandrasekhar limit, ignite carbon under degenerate conditions and explode as a SN Ia (Webbink \cite{webbink84}; Iben Tutukov \cite{iben84}) )."1033 One of the best known candidate system for this double degenerate merger scenario is the sdB+WD binary 11930-2752. (Maxted et al. 2000a::, One of the best known candidate system for this double degenerate merger scenario is the sdB+WD binary $+$ 2752 (Maxted et al. \cite{maxted00a};1034 Geter et al. 2007)., Geier et al. \cite{geier07}) ).1035 Mereghetti et al. (2009)), Mereghetti et al. \cite{mereghetti09}) )1036" showed that in the X-ray binary 449798 a massive (>1.2 M.) white dwarf aceretes matter from a closely orbiting subdwarf O companion,"," showed that in the X-ray binary 49798 a massive $>1.2\,{\rm M_{\odot}}$ ) white dwarf accretes matter from a closely orbiting subdwarf O companion."1037 The predicted amount of accreted material is sufficient for the WD to reach the Chandrasekhar limit., The predicted amount of accreted material is sufficient for the WD to reach the Chandrasekhar limit.1038 This makes 449798 another candidate Ila progenitor. should the companion be a C/O white dwarf (Wang et al. 2009)).," This makes 49798 another candidate Ia progenitor, should the companion be a C/O white dwarf (Wang et al. \cite{wang09}) )."1039 SN Ia play a key role in the study of cosmic evolution., SN Ia play a key role in the study of cosmic evolution.1040 They are utilised as standard candles for determining the cosmological parameters, They are utilised as standard candles for determining the cosmological parameters1041"constant, c the speed of light, kg the Boltzmann constant and H(z) is the Hubble parameter at the emission redshift.","constant, $c$ the speed of light, $\kb$ the Boltzmann constant and $H(z)$ is the Hubble parameter at the emission redshift."1042" For a universe and neglecting radiation energy density, the Hubble parameter can be expressed as: Introducing the mass fraction relative to the total baryon mass fz,, the neutral hydrogen number density relative fluctuations can be written as, and the corresponding 21 cm emission temperature can be written as: where Qs,Perit are PHely the present day mean baryon cosmological and critical densities, my is the hydrogen atom mass, and à is the density fluctuations."," For a universe and neglecting radiation energy density, the Hubble parameter can be expressed as: Introducing the mass fraction relative to the total baryon mass $\gHI$, the neutral hydrogen number density relative fluctuations can be written as, and the corresponding 21 cm emission temperature can be written as: where $\Omega_B, \rho_{crit}$ are respectively the present day mean baryon cosmological and critical densities, $m_{H}$ is the hydrogen atom mass, and $\frac{\delta \rho_{H_I}}{\bar{\rho}_{H_I}}$ is the density fluctuations."1043" The present day neutral hydrogen fraction fy,(0) present in local galaxies has been measured to be ~1% of the baryon density (Zwaanetal.(2005)):: The neutral hydrogen fraction is expected to increase with redshift, as gas is used in star formation during galaxy formation and evolution."," The present day neutral hydrogen fraction $\gHI(0)$ present in local galaxies has been measured to be $\sim 1\%$ of the baryon density \citep{zwann.05}: The neutral hydrogen fraction is expected to increase with redshift, as gas is used in star formation during galaxy formation and evolution."1044" Study of Lyman-a absorption indicate a factor 3 increase in the neutral hydrogen fraction at z=1.5 in the intergalactic medium (Wolfetal.(2005)),, compared to its present day value fy,(z=1.5)~0.025."," Study of $\alpha$ absorption indicate a factor 3 increase in the neutral hydrogen fraction at $z=1.5$ in the intergalactic medium \citep{wolf.05}, compared to its present day value $\gHI(z=1.5) \sim 0.025$."1045" The 21 cm brightness temperature and the corresponding power spectrum can be written as (Barkana&Loeb(2007) and Madatetal. (1997)))Pr, The table 2 shows the VQ,mean +2321 +cm Qnbrightness temperature for the standard cosmology and either a constant mass fraction fg,=0.01, or linearly increasing fy,~0.008(1+ z)."," The 21 cm brightness temperature and the corresponding power spectrum can be written as \cite{barkana.07} and \cite{madau.97}) ): The table \ref{tabcct21} shows the mean 21 cm brightness temperature for the standard cosmology and either a constant mass fraction $\gHI = 0.01$, or linearly increasing $\gHI \simeq 0.008 \times (1+z) $ ."1046" Figure 1 shows the 21 cm emission power spectrum at several redshifts, with a constant neutral fraction at (fu,= 0.02)."," Figure \ref{figpk21} shows the 21 cm emission power spectrum at several redshifts, with a constant neutral fraction at $\gHI=0.02$ )."1047 The matter power spectrum has been computed using the Eisenstein&Hu(1998) parametrisation., The matter power spectrum has been computed using the \cite{eisenhu.98} parametrisation.1048" The correspondence with the angular scales is also shown for the standard WMAP cosmology, according to the relation: where k is the comoving wave vector and dA4(z) is the angular diameter distance."," The correspondence with the angular scales is also shown for the standard WMAP cosmology, according to the relation: where $k$ is the comoving wave vector and $ \dang(z) $ is the angular diameter distance."1049 We introduce briefly here the principles of interferometric observations and the definition of quantities useful for our calculations., We introduce briefly here the principles of interferometric observations and the definition of quantities useful for our calculations.1050" Interested reader may refer to (Thompson,Moran&Swenson(2001)) for a detailed and complete presentation of observation methods and signal processing in radio astronomy.", Interested reader may refer to \citep{radastron} for a detailed and complete presentation of observation methods and signal processing in radio astronomy.1051" In astronomy we are usually interested in measuring the sky emission intensity, I(G,4) in a given wave band, as a function of the sky direction."," In astronomy we are usually interested in measuring the sky emission intensity, $I(\vec{\Theta},\lambda)$ in a given wave band, as a function of the sky direction."1052" In radio astronomy and interferometry in particular, receivers are sensitive to the sky emission complex amplitudes."," In radio astronomy and interferometry in particular, receivers are sensitive to the sky emission complex amplitudes."1053" However, for most sources, the phases vary randomly with a spatial correlation length significantly smaller than the instrument resolution."," However, for most sources, the phases vary randomly with a spatial correlation length significantly smaller than the instrument resolution."1054" A single receiver canA) be characterized by its angular complex amplitude response B(G,v) andits position 7 in a reference frame."," A single receiver can be characterized by its angular complex amplitude response $B(\vec{\Theta},\nu)$ andits position $\vec{r}$ in a reference frame."1055" the waveform complex amplitude s measured by the receiver, for each frequency can be written as a function of the electromagnetic wave vector Kem(6,A): We have set the electromagnetic (EM) phase origin at the center of the coordinate frame and the EM wave is related to the wavelength 2 through the usual equation vector|kgy|= 2π/Λ."," the waveform complex amplitude $s$ measured by the receiver, for each frequency can be written as a function of the electromagnetic wave vector $\vec{k}_{EM}(\vec{\Theta}, \lambda) $: We have set the electromagnetic (EM) phase origin at the center of the coordinate frame and the EM wave vector is related to the wavelength $\lambda$ through the usual equation $ | \vec{k}_{EM} | = 2 \pi / \lambda $ ."1056" The receiver beam or antenna lobe L(@,A) corresponds to the receiver intensity response:"," The receiver beam or antenna lobe $L(\vec{\Theta},\lambda)$ corresponds to the receiver intensity response:"1057Telescope (NTT) telescope at La Silla Observatory was used.,Telescope (NTT) telescope at La Silla Observatory was used.1058 With the Large Field setup we achieved a 4.9x arcminute field of view and a pixel scale of 0.288 arcsec/pixel.," With the Large Field setup we achieved a $4.9 \times10594.9$ arcminute field of view and a pixel scale of 0.288 arcsec/pixel."1060 During (wo photometric nights we obtained deep Js and A5 observations of five fields in the LMC. with each field containing at least a dozen RRL stars.," During two photometric nights we obtained deep $Js$ and $Ks$ observations of five fields in the LMC, with each field containing at least a dozen RRL stars."1061 Fig., Fig.1062 1. displays the location ol these fields in the LMC., \ref{figfields} displays the location of these fields in the LMC.1063 On the second night. fields 1 and 2 were overlapped with field 3a.," On the second night, fields 1 and 2 were overlapped with field 3a."1064 Detailed information on each field is given in Table 1.., Detailed information on each field is given in Table \ref{tabfields}.1065 In order to take into consideration (he rapid sky level variations in the infrared passbancl. we used a dithering technique.," In order to take into consideration the rapid sky level variations in the infrared passband, we used a dithering technique."1066 Total integration times were up to 40 minutes for As. and 11 minutes for the Js band.," Total integration times were up to 40 minutes for $Ks$ , and 11 minutes for the $Js$ band."1067 The pipeline developed in the course of Araucaria Project was used for all the reductions and calibrations., The pipeline developed in the course of Araucaria Project was used for all the reductions and calibrations.1068 First. the subtraction of sky level was applied in a (vo-step process which includes the masking of stars with the IRAF xdimsum package (Pietrzvisski Gieren 20022).," First, the subtraction of sky level was applied in a two-step process which includes the masking of stars with the IRAF xdimsum package (Pietrzyńsski Gieren 2002a)."1069 Next. each single image was flat fielded and stacked into (he final deep field.," Next, each single image was flat fielded and stacked into the final deep field."1070 PSF photometry. including aperture corrections. was performed in (he same wav as described in Pietrzviisski. Gieren Udalski (2002¢).," PSF photometry, including aperture corrections, was performed in the same way as described in Pietrzyńsski, Gieren Udalski (2002c)."1071 The calibration of the photometry onto the standard svstem was based on observations of 14 standard stars from the UINXIRT list (Lasvarden οἱ al., The calibration of the photometry onto the standard system was based on observations of 14 standard stars from the UKIRT list (Hawarden et al.1072 2001)., 2001).1073 All of them were observed together wilh the target fields during photometric conditions at different airmasses., All of them were observed together with the target fields during photometric conditions at different airmasses.1074 Thanks io the large number of standard: stars observed along with the science target fields. the accuracy of our photometry zero point was estimated to be as good as 0.02 mag.," Thanks to the large number of standard stars observed along with the science target fields, the accuracy of our photometry zero point was estimated to be as good as 0.02 mag."1075 Our calibrated photometric magnitudes were compared with the 2\TASS catalogue for common stars. which gave us a zero point difference.," Our calibrated photometric magnitudes were compared with the 2MASS catalogue for common stars, which gave us a zero point difference."1076 Also stars that were measured on both nights and cross-identified on different [ields were compared (SC5-FI + SC5-EII with SC5-FILL. and on following nights).," Also stars that were measured on both nights and cross-identified on different fields were compared (SC5-FI + SC5-FII with SC5-FIII, and SC7-FV, on following nights)."1077 The results of comparison of zero point differences between our work and 2\TASS are shown in Table 2.., The results of comparison of zero point differences between our work and 2MASS are shown in Table \ref{tab2mass}.1078 The increase in difference between IX-band observations for field 3a maa be caused by larger cerowcding and less aceiraey of 2M1ASS photometry in (hese regions., The increase in difference between K-band observations for field 3a may be caused by larger crowding and less accuracy of 2MASS photometry in these regions.1079 The Red Clamp (RC) brightness was also compared will previously published data (Pielrzvisski. Gieren Udalski 2003).," The Red Clump (RC) brightness was also compared with previously published data (Pietrzyńsski, Gieren Udalski 2003)."1080 Results of the determination of the RC star mean brightness in each of our fields are eiven in Tab. 33.., Results of the determination of the RC star mean brightness in each of our fields are given in Tab. \ref{tabrc}.1081 They compare very. well with the values found by Pietrzvisski Gieren (20020) in their observed fields (./=17.50740.009. dv=16.895+ 0.007).," They compare very well with the values found by Pietrzyńsski Gieren (2002a) in their observed fields $J=17.507 \pm 0.009$, $K=16.895 \pm 0.007$ )."1082 The calibrated near-inlrared magnitudes for all RRL stars identified in our fields are presented in Tab. 4.., The calibrated near-infrared magnitudes for all RRL stars identified in our fields are presented in Tab. \ref{tabrawobs}.1083 The sample of 65 RRL starswe have observed in our chosen SOFI/NTT fields were, The sample of 65 RRL starswe have observed in our chosen SOFI/NTT fields were1084"~ 0.14 Mo, and the star has undergone 11 thermal pulses).","$\sim$ 0.14 $_{\odot}$, and the star has undergone 11 thermal pulses)."1085 Meanwhile the ?He surface abundance has slightly decreased from 2.74x10 to 2.67x10*., Meanwhile the $^3$ He surface abundance has slightly decreased from $2.74 \times 10^{-4}$ to $2.67 \times 10^{-4}$.1086 We wish to emphasize an interesting result obtained for the 2.0 Mc model that was computed up to the AGB tip with thermohaline mixing but without rotation., We wish to emphasize an interesting result obtained for the 2.0 $_{\odot}$ model that was computed up to the AGB tip with thermohaline mixing but without rotation.1087 This model did undergo 11 thermal pulses in total., This model did undergo 11 thermal pulses in total.1088" After the 9th thermal pulse third dredge-up occurred, that slightly increased the ΙΟ surface abundance as well as the carbon isotopic ratio."," After the 9th thermal pulse third dredge-up occurred, that slightly increased the $^{12}$ C surface abundance as well as the carbon isotopic ratio."1089 During the following interpulse phase this ratio was slightly lowered under the effect of thermohaline mixing., During the following interpulse phase this ratio was slightly lowered under the effect of thermohaline mixing.1090" Quantitatively, the carbon isotopic ratio increased from 19.6 to 21.33 between the end of the second dredge-up and the AGB tip (see also Fig.18 and discussion in 4.2)."," Quantitatively, the carbon isotopic ratio increased from 19.6 to 21.33 between the end of the second dredge-up and the AGB tip (see also \ref{fig_c1213_PNe} and discussion in 4.2)."1091 This could indicate that thermohaline mixing does favour the occurrence of third dredge-up., This could indicate that thermohaline mixing does favour the occurrence of third dredge-up.1092 This will be investigated further in a future paper., This will be investigated further in a future paper.1093" By definition, intermediate-mass stars are objects that ignite central helium-burning in a non-degenerate core at relatively low luminosity on the RGB, well before the HBS reaches the mean molecular weight discontinuity caused by the first dredge-up."," By definition, intermediate-mass stars are objects that ignite central helium-burning in a non-degenerate core at relatively low luminosity on the RGB, well before the HBS reaches the mean molecular weight discontinuity caused by the first dredge-up."1094" In other words, these objects do not go through a bump on their short ascend of the RGB, and thus do not undergo thermohaline mixing at that phase."," In other words, these objects do not go through a bump on their short ascend of the RGB, and thus do not undergo thermohaline mixing at that phase."1095" We should note, however, that as in the previous cases, rotation-induced mixing can not be neglected from the whole picture."," We should note, however, that as in the previous cases, rotation-induced mixing can not be neglected from the whole picture."1096 We refer to for a discussion of the global effects of rotation on the evolution and asterosismic properties of intermediate-mass red giants?)., We refer to for a discussion of the global effects of rotation on the evolution and asterosismic properties of intermediate-mass red giants.1097. Its impact on the chemical structure of a 4.0 M. star at turnoff can be seen in Fig. 13.., Its impact on the chemical structure of a 4.0 $_{\odot}$ star at turnoff can be seen in Fig. \ref{fig:profils_abon_rotdiff_4}.1098" Note that in thismass range the base of the convective envelope reaches the ??Na plateau during the first dredge-up, leading to an increase of the surface abundance of this element both in the non-rotating and rotating cases."," Note that in thismass range the base of the convective envelope reaches the $^{23}$ Na plateau during the first dredge-up, leading to an increase of the surface abundance of this element both in the non-rotating and rotating cases."1099 Overall rotation-induced mixing leads to stronger modifications of the stellar chemical properties when the star becomes a giant as its convective envelope dredges-up nuclearly processed material., Overall rotation-induced mixing leads to stronger modifications of the stellar chemical properties when the star becomes a giant as its convective envelope dredges-up nuclearly processed material.1100" At the end of the dredge-up for the 4 Ms models, the surface ?He abundance is 1.1x107* and 8.4x10? in the non-rotating and rotating (initial rotation velocity of 300 km s-!) models respectively, while the carbon isotopic ratio is 20.5 or 14 respectively, and N(Li) is 1.3 or -].8."," At the end of the dredge-up for the 4 $_{\odot}$ models, the surface $^3$ He abundance is $1.1 \times 10^{-4}$ and $8.4 \times 10^{-5}$ in the non-rotating and rotating (initial rotation velocity of 300 km $^{-1}$ ) models respectively, while the carbon isotopic ratio is 20.5 or 14 respectively, and N(Li) is 1.3 or -1.8."1101" We computed the first 11 thermal pulses for the 4 Mo models without and with rotation-induced mixing, including thermohaline mixing in both cases."," We computed the first 11 thermal pulses for the 4 $_{\odot}$ models without and with rotation-induced mixing, including thermohaline mixing in both cases."1102" A strong Li increase at the stellar surface is obtained during the first thermal pulses, and then lithium production levels off at a value of the order of N(Li)=2.2."," A strong Li increase at the stellar surface is obtained during the first thermal pulses, and then lithium production levels off at a value of the order of N(Li)=2.2."1103 This agrees with predictions., This agrees with predictions.1104" Again, a detailed exploration of the TP-AGB phase for intermediate-mass stars is postponed to a further paper."," Again, a detailed exploration of the TP-AGB phase for intermediate-mass stars is postponed to a further paper."1105 We now test the theoretical predictions of our models with respect to observations of relevant chemical elements in stars at different evolution stages., We now test the theoretical predictions of our models with respect to observations of relevant chemical elements in stars at different evolution stages.1106" In Table 2 we give the surface carbon isotopic ratio as well as surface abundances of ?7Li, ?Be, [C/Fe], [N/Fe], and [Na/Fe], at the end of the first dredge-up, at the RGB tip, and at the end of the second dredge-up, for each of the models we have computed."," In Table \ref{tablesurfabundances} we give the surface carbon isotopic ratio as well as surface abundances of $^{7}$ Li, $^{9}$ Be, [C/Fe], [N/Fe], and [Na/Fe], at the end of the first dredge-up, at the RGB tip, and at the end of the second dredge-up, for each of the models we have computed."1107" In this table and in the following figures all the predictions correspond to models computed with a value of C,—10? for thermohaline mixing (without or with rotation-induced mixing).", In this table and in the following figures all the predictions correspond to models computed with a value of $_{\rm t} = 10^3$ for thermohaline mixing (without or with rotation-induced mixing).1108" As underlined in 3, we did not include parametric convectively induced extra-mixing during the TP-AGB phase so that our models are not expected to undergo third dredge-up and to mimic carbon-rich stars."," As underlined in 3, we did not include parametric convectively induced extra-mixing during the TP-AGB phase so that our models are not expected to undergo third dredge-up and to mimic carbon-rich stars."1109 As already mentioned the predictions of the present rotating models have been successfully compared to Li and Be observations along the whole evolutionary sequence of the Galactic open cluster IC 4651 (turnoff mass 1.8 Mo) by 14.., As already mentioned the predictions of the present rotating models have been successfully compared to Li and Be observations along the whole evolutionary sequence of the Galactic open cluster IC 4651 (turnoff mass 1.8 $_{\odot}$ ) by .1110 They account very nicely for all the Li and Be features observed in this cluster., They account very nicely for all the Li and Be features observed in this cluster.1111to show evidence of such mass transfer activity in their lighteurves.,to show evidence of such mass transfer activity in their lightcurves.1112 A number of EcB appear to lie on the cluster Binary Main Sequence (BAIS) ancl as such all are very likely members of 47 Tuc., A number of EcB appear to lie on the cluster Binary Main Sequence (BMS) and as such all are very likely members of 47 Tuc.1113 Detached svstems are also seen in (he sample (V39. V41. V69. V78. δι V39 and V93).," Detached systems are also seen in the sample (V39, V41, V69, V78, V84, V89 and V93)."1114 Of these. four do not show detectable secondary eclipses to our rns level (V69. V7s. V89. V93). and thus could conceivably be orbited bv low luminosity companions. most likely M-dwarls.," Of these, four do not show detectable secondary eclipses to our rms level (V69, V78, V89, V93), and thus could conceivably be orbited by low luminosity companions, most likely M-dwarfs."1115 Our data for V78 and V93 is very limited. with onlv one eclipse visible across our temporal range.," Our data for V78 and V93 is very limited, with only one eclipse visible across our temporal range."1116 Our period estimates for these (wo variables are therefore not well determined., Our period estimates for these two variables are therefore not well determined.1117 We have estimated a period for these two stus which would hold if all other eclipses occured during cloud or davlieht., We have estimated a period for these two stars which would hold if all other eclipses occured during cloud or daylight.1118 Further observations are required to derive an accurate period., Further observations are required to derive an accurate period.1119 If these stars are indeed orbited by M-Diwarls. (hese variables would be important to determine (he survivability and long-term stability of such low-mass companions inside eglobular clusters (Adams&Latehlin2003).," If these stars are indeed orbited by M-Dwarfs, these variables would be important to determine the survivability and long-term stability of such low-mass companions inside globular clusters \citep{AL03}."1120. We present phase wrapped lighteurves of these (wo special cases. in Fig.l3.. with the eclipses plotted more clearly than in the general lishteurve database figures.," We present phase wrapped lightcurves of these two 'special cases' in \ref{Mdwarf}, with the eclipses plotted more clearly than in the general lightcurve database figures."1121 V13 also shows an apparent variation al L.015d. as well as the longer period for which only one eclipse is seen.," V78 also shows an apparent variation at 1.015d, as well as the longer period for which only one eclipse is seen."1122 This is shown in Fig.8 (wo plots lor VT3). and as the period is so close to 1 dax. it is almost certainly due (to terrestrial effects.," This is shown in \ref{VarPlot2} (two plots for V78), and as the period is so close to 1 day, it is almost certainly due to terrestrial effects."1123 It is included for completeness., It is included for completeness.1124 The lighteurve data suggest that the companion sizes are approximately 0.25-0.3 Solar radius. assuming a mid-to late IxX-tvpe primary at the distance of 47 Tuc.," The lightcurve data suggest that the companion sizes are approximately 0.25-0.3 Solar radius, assuming a mid-to late K-type primary at the distance of 47 Tuc."1125 The rest of our EcD sample are detached binaries on the cluster BMS., The rest of our EcB sample are detached binaries on the cluster BMS.1126 The apparent frequency. of the occurence of detectable 47 Tuc contact binaries in the field is 21/124073 = 07250.4x 10.) which is slightly higher. but consistent with. the estimate of 1x10. ! presented in Kaluznyetal.(1998)... and is more than an order of magnitude lower than that observed in the core of 47Tuc (Albrowetal.2001).. and in fields containing Galactic open clusters (xaluzny&Iucinski1993). and OGLE fields located," The apparent frequency of the occurence of detectable 47 Tuc contact binaries in the field is 21/124073 $\thickapprox$ $\pm$ $\times$ $^{-4}$, which is slightly higher, but consistent with, the estimate of $\times$ $^{-4}$ presented in \citet{Kal98}, and is more than an order of magnitude lower than that observed in the core of 47Tuc \citep{Alb01}, and in fields containing Galactic open clusters \citep{KR93} and OGLE fields located"1127fud 180 (conservative) to 1000 (optimistic) clusters with a total radio luminosity of ΕΕ within this cosmological volume.,find 180 (conservative) to 1000 (optimistic) clusters with a total radio luminosity of $10^{25}W/Hz$ within this cosmological volume.1128 We also sce from Fieure 12. that the huuinositv function of halos increases from :=1 to Ξ0., We also see from Figure \ref{fig:lum_func} that the luminosity function of halos increases from $z=1$ to $z=0$.1129 However. if plotted using proper volumes. the factor of 8 brines the two luminosity functions πιο closer together.," However, if plotted using proper volumes, the factor of 8 brings the two luminosity functions much closer together."1130 Therefore the proper number density of radio relics seclus to be fairly constant through cosmic time., Therefore the proper number density of radio relics seems to be fairly constant through cosmic time.1131 This is an unexpected result. aud encouraging for moderate redshift studies of radio relies;," This is an unexpected result, and encouraging for moderate redshift studies of radio relics."1132 We note here that the frequency at which telescopes receive this svuchrotrou Cluission changes as a fiction of the emitters redshift., We note here that the frequency at which telescopes receive this synchrotron emission changes as a function of the emitter's redshift.1133 Therefore wheu deriving the radio Iuminositv of au object at redshift z. we use v=1.1Cz(1|2).," Therefore when deriving the radio luminosity of an object at redshift $z$, we use $\nu =11341.4~\mathrm{GHz}~(1+z)$."1135 Because of this. the emitted power is actually decreased since P464iκpoU?s where szm2 for strone shocks.," Because of this, the emitted power is actually decreased since $P_{1.4GHz}\propto \nu^{-s/2}$ where $s\approx2$ for strong shocks."1136 The power emitte iu the clusters frame is therefore substautially larger than what is shown in Figure 12.., The power emitted in the cluster's frame is therefore substantially larger than what is shown in Figure \ref{fig:lum_func}.1137 The similar Iuuünosity function is therefore a product of the increased merger and accretion activity at higher redshift compared to that at.=O)., The similar luminosity function is therefore a product of the increased merger and accretion activity at higher redshift compared to that at $z=0$.1138 Iu order to compared.c our results to previous shock studies. we have caleulated the kinetic energv fux hrough shocks. as shown in figure 13..," In order to compare our results to previous shock studies, we have calculated the kinetic energy flux through shocks, as shown in figure \ref{fig:energy_radio_flux}."1139 The left two »uels show the kinetic ejiergv flux as a function of Mach uuniber in the reliediL ancl relie200 Snulatious. respectively.," The left two panels show the kinetic energy flux as a function of Mach number in the $relic64$ and $relic200$ simulations, respectively."1140 The right paτος dustead show the radio Cluission as a fuuctiou of Mach umber., The right panels instead show the radio emission as a function of Mach number.1141" While the lack lines denote all teiveratures, we also show the weakKkdowan iu terms of the pre-shock temperature."," While the black lines denote all temperatures, we also show the breakdown in terms of the pre-shock temperature."1142 The οποιος energy flux results here cau be directly compared o Figure 6 of ?.. Figure 10 of ?.. Figure 1H of ?.. and can also be compared after unit conversions to Figure 6 of ?..," The kinetic energy flux results here can be directly compared to Figure 6 of \citet{Ryu:2003aa}, Figure 10 of \citet{Skillman:2008aa}, Figure 11 of \citet{Vazza:2009aa}, and can also be compared after unit conversions to Figure 6 of \citet{Pfrommer:2006aa}."1143 Even though these simulations all vary in size aud adopted cosmological parameters. the simularitics im the kinetic eunergv flux processed by shocks is quite strong.," Even though these simulations all vary in size and adopted cosmological parameters, the similarities in the kinetic energy flux processed by shocks is quite strong."1144 This sueecstsCoco that the underline shock characteristics are quite well understood even if the particular racio Cluission models vary., This suggests that the underlying shock characteristics are quite well understood even if the particular radio emission models vary.1145 Iu the right panels of 13.. we cau see that there is a larger difference between the two simulations preseuted here iu terms of the radio enüssion.," In the right panels of \ref{fig:energy_radio_flux}, we can see that there is a larger difference between the two simulations presented here in terms of the radio emission."1146 This is likely due to the varviug mass scales present in the simulations., This is likely due to the varying mass scales present in the simulations.1147 We have also subsampled the ο simulation iuto random (61Mpc/h)? domains aud found that a major contribution is confined to oue of these subdomains.," We have also subsampled the $relic200$ simulation into random $(\mathrm{641148 Mpc/h})^3$ domains and found that a major contribution is confined to one of these subdomains."1149 Oue of the earliest studies of shocks in a cosmological contest is found in 7.. where the authors found. similar shock structure and kinetic cnerey flux trends as is seen in this study. though iu a uuigrid coutext.," One of the earliest studies of shocks in a cosmological context is found in \citet{Miniati:2000aa}, where the authors found similar shock structure and kinetic energy flux trends as is seen in this study, though in a unigrid context."1150 They. too. found that iterinediate Mach: uunuber shocks are responsible for processing the majority of kinetic energy.," They, too, found that intermediate Mach number shocks are responsible for processing the majority of kinetic energy."1151 Iu a pioneering work. ? studied. the injection aud evolution of cosmic rav clectrons.," In a pioneering work, \citet{Miniati:2001ab}1152 studied the injection and evolution of cosmic ray electrons."1153 Using a framework. to follow the cosmic rav distribution. they presented a radio power - core temperature relationship that shows strong similarity to what we have found with respect to cluster mass and N-ray hunuinositv. incliding a larger amount of scatter from cluster-to-cluster.," Using a framework to follow the cosmic ray distribution, they presented a radio power - core temperature relationship that shows strong similarity to what we have found with respect to cluster mass and X-ray luminosity, including a larger amount of scatter from cluster-to-cluster."1154 Even though the resolution was modest compared to studies here. many of the primary characteristics of the radio emission are sul.," Even though the resolution was modest compared to studies here, many of the primary characteristics of the radio emission are similar."1155 Mach of our work presented here cau be compared with that of ὃν, Much of our work presented here can be compared with that of \citet{Hoeft:2008aa}.1156 We use the same radio onuission uodel. but instead apply it to AMIR simulations as opposed to smootled particle hivdrodyuauic simulations.," We use the same radio emission model, but instead apply it to AMR simulations as opposed to smoothed particle hydrodynamic simulations."1157 Iu particular. we cau compare our radio relic Inuinosity ction in Figure 12 to their Figure 9.," In particular, we can compare our radio relic luminosity function in Figure \ref{fig:lum_func} to their Figure 9."1158 After accounting or the different normalization. we find that we have nore objects at ο/IT+.," After accounting for the different normalization, we find that we have more objects at $\sim 10^{25} W/Hz$."1159 However. this result is from a sinall umber of objects in our simulations aud therefore uture simulations witha larger sample of galaxy clusters are needed.," However, this result is from a small number of objects in our simulations and therefore future simulations with a larger sample of galaxy clusters are needed."1160 Iu ?.. the authors studied the acceleration aud emission xoperties of cosmic rav clectrous and protous iu a sinoothed particle hivdrodyaanices setting which focused on a set of high resolution galaxy. clusters.," In \citet{Pfrommer:2008aa}, the authors studied the acceleration and emission properties of cosmic ray electrons and protons in a smoothed particle hydrodynamics setting which focused on a set of high resolution galaxy clusters."1161 Maux of the sale characteristics of galaxy cluster radio relic cussion that we found im this study are consistent with their results., Many of the same characteristics of galaxy cluster radio relic emission that we found in this study are consistent with their results.1162 The morphology of the radio relic cussion is very simular to our results. though since they follow the electron population through time the ciissiou is more diffuse compared to our simulated clusters.," The morphology of the radio relic emission is very similar to our results, though since they follow the electron population through time the emission is more diffuse compared to our simulated clusters."1163 Iu another paper iu the same series. 2 study the scaling relationship between the radio svuchrotron. @auunarayv. and inverse Compton oenüssion from the same set of ealaxv clusters.," In another paper in the same series, \citet{Pfrommer:2008ab} study the scaling relationship between the radio synchrotron, gamma-ray, and inverse Compton emission from the same set of galaxy clusters."1164 Their results when fitting the scaling releiouship between radio svuchrotron oeniüssion al cluster mass eive a significautly shallower slope of 11.5., Their results when fitting the scaling relationship between radio synchrotron emission and cluster mass give a significantly shallower slope of $1-1.5$.1165 However. due to t1ο πα ΠΠνα of clusters iu their study. it is differIt to tell if there is a imeaninetu difference between their restIts and the oues presentcc here.," However, due to the small number of clusters in their study, it is difficult to tell if there is a meaningful difference between their results and the ones presented here."1166 In future wor sat would be useful to un a series of high resolution AMA. simulations using our methods to conrpare to their results., In future work it would be useful to run a series of high resolution AMR simulations using our methods to compare to their results.1167 Qur study has shown that nearly every cluster has radio emission and displavs sigus of radio relics at some stage in their evolution., Our study has shown that nearly every cluster has radio emission and displays signs of radio relics at some stage in their evolution.1168 When aud where this radio Cluission occurs. however. Is very sensitive to the morecr and evolutionary state of the cluster.," When and where this radio emission occurs, however, is very sensitive to the merger and evolutionary state of the cluster."1169 Current studies of radio relies have been confined to pointer observations of nearby. massive clusters. offen based on strong N-rav emission.," Current studies of radio relics have been confined to pointed observations of nearby, massive clusters, often based on strong X-ray emission."1170 While this observational strategy does conformi to our general results found im nass and N-ray scaling relationships. we lave determiüuce hat uot all X-rav luminous or massive clusters have sjeuificaut relic enüssiou.," While this observational strategy does conform to our general results found in mass and X-ray scaling relationships, we have determined that not all X-ray luminous or massive clusters have significant relic emission."1171 It is instead heavily biase owards disturbed. mereie clusters.," It is instead heavily biased towards disturbed, merging clusters."1172 Because the surface xiehtuess of these relies is low duc to their exteudie ature. huge surveys with near-future telescopes are uulikely to viell sereudipitous discoveries of cluster radio enmuüssion.," Because the surface brightness of these relics is low due to their extended nature, large surveys with near-future telescopes are unlikely to yield serendipitous discoveries of cluster radio emission."1173 Lhnustead. the focus should be on deep. uultiwaveleugth. large feld-ofview observations with seusitivitv to extended diffuse radio emission of disturbed N-rav clusters.," Instead, the focus should be on deep, multiwavelength, large field-of-view observations with sensitivity to extended diffuse radio emission of disturbed X-ray clusters."1174 Additionally. studies ust inchicde regions away from the peak N-rav endssion.," Additionally, studies must include regions away from the peak X-ray emission."1175 As was secu in Section ??..," As was seen in Section \ref{sec:individual_object_properties}, ,"1176"In the case of 0,=0. we have pr=cos).","In the case of $\theta_v=0$, we have $\mu=\cos\theta$."1177" It should be noted that there is an interesting phenomenon. the values of 50 increase with the anele 0. ie. there is a characteristic angle 0.. at which the value 5.0,=1. when 0<0, the value 50«1. aud when 0>0, the value 560>l."," It should be noted that there is an interesting phenomenon, the values of $\gamma\theta$ increase with the angle $\theta$, i.e. there is a characteristic angle $\theta_{\star}$ , at which the value $\gamma_{\star}\theta_{\star}=1$, when $\theta<\theta_{\star}$ the value $\gamma\theta<1$, and when $\theta> \theta_{\star}$ the value $\gamma\theta>1$."1178" Tt is obvious that the main contribution of cuuission comes from the region 0<O,. so O, Is an important quantitv."," It is obvious that the main contribution of emission comes from the region $\theta\leq \theta_{\star}$, so $\theta_{\star}$ is an important quantity."1179" It can be shown that when 1πτι-yoyLiaSony3,RM0NÉS! hours. the value 0, θε. and when T€Ty=5.2(02)yh{ο.Pg!1/3;Qsibyστ)Ui(SE23 davs.dass thevun valueN 0,_=}LRTSEESAdy{CondléiNKk)0,ουTy- 0j."," It can be shown that when $T\leq T_1 \equiv11801.7(\frac{\epsilon_{0,54}}{n_1})^{1/3}(\frac{\theta_c}{0.02})^{8/3}$ hours, the value $\theta_{\star}=10^{-1.27}(\frac{\epsilon_{0,54}}{n_1})^{-1/8}1181T_{day}^{3/8}\leq \theta_c$ , and when $T\leq T_2 \equiv 5.2\times1182(0.2)^{k/3}(\frac{\epsilon_{0,54}}{n_1})^{1/3}1183(\frac{\theta_c}{0.02})^{k/3}(\frac{\theta_j}{0.1})^{(8-k)/3}$ days, the value $\theta_{\star}=10^{-1.27\times11848/(8-k)}(\frac{\epsilon_{0,54}}{n_1})1185^{-1/(8-k)}\theta_c^{-k/(8-k)}T_{day}^{3/(8-k)}\leq \theta_j$ ."1186" Taking equation (5) and the approximate expression jo(207)| for P< θα—pcmAP for 0> 0,. we can eet the analytical results: (1) when T<Ti. the observed fux ΕνxT?11 (2) when Tj€TxTs. he flux F,~T=o for k<LH or F,xTo! or kᾗ- (3) when To>T». the fux FyxT41,"," Taking equation (5) and the approximate expression $1-\beta\mu \simeq1187(2\gamma^2)^{-1}$ for $\theta<\theta_{\star}$, or $1-\beta\mu \simeq1188\frac{1}{2}\theta^2$ for $\theta>\theta_{\star}$ , we can get the analytical results: (1) when $T\leq T_1$, the observed flux $F_{\nu}\propto T^{-3(p-1)/4}$; (2) when $T_1\leq T \leq T_2$, the flux $F_{\nu}\propto T^{-\frac{3(2p+k-2)}{8-k}}$ for $k<\frac{8}{p+4}$, or $F_{\nu} \propto T^{-3p/4}$ for $k>\frac{8}{p+4}$; (3) when $T>T_2$, the flux $F_{\nu}\propto T^{-3p/4}$."1189 From this mTresult we sec that. for simaller value of &. the rausition of the afterglow light curve index frou Sui ο - is eradual aud smooth with a timescale of about Ty. while for arecr values of &. the transition is rapid with a timescale of about Ti.," From this result we see that, for smaller value of $k$, the transition of the afterglow light curve index from $-\frac{3(p-1)}{4}$ to $-\frac{3p}{4}$ is gradual and smooth with a timescale of about $T_2$, while for larger values of $k$, the transition is rapid with a timescale of about $T_1$."1190" Tn order to verity the above results. we also make a uunereal calculation for the case 0,=0."," In order to verify the above results, we also make a numerical calculation for the case $\theta_v=0$."1191 Fig.2 eives our results., Fig.2 gives our results.1192 It is obvious that the nunuercal results are consistent with the analytical results. for larger value of Αν the steepenius of the light. curve is more rapidly.," It is obvious that the numerical results are consistent with the analytical results, for larger value of $k$, the steepening of the light curve is more rapidly."1193 We suggest this may explain some afterelow light curves which decay rapidly audhave no breaks. since for larger value of k the transition time ( T3) is earlier than our first observation tie.," We suggest this may explain some afterglow light curves which decay rapidly andhave no breaks, since for larger value of $k$ the transition time $\sim T_1$ ) is earlier than our first observation time."1194 However. it should be noted that the appearance of the carly break in the lieht curve (correspoucding to the time when ~~ 7.1) is due to the assimued cnerey distribution function (equation (10)). and the sharpuess of this break is primarily depeudent on the discontiuuitv in slope of € for theidealized model of equation (10) a ()—0..," However, it should be noted that the appearance of the early break in the light curve (corresponding to the time when $\gamma\sim1195\theta_c^{-1}$ ) is due to the assumed energy distribution function (equation (10)), and the sharpness of this break is primarily dependent on the discontinuity in slope of $\epsilon$ for theidealized model of equation (10) at $\theta=\theta_c$."1196" Tt is obvious that for a realistic energy. distribution. the transition of € from roughly constant for 0«0. to eX0* for 0c0, should be smooth."," It is obvious that for a realistic energy distribution, the transition of $\epsilon$ from roughly constant for $\theta < \theta_c$ to $\epsilon\propto\theta^{-k}$ for $\theta >1197\theta_c$ should be smooth."1198 Therefore this break may be washed out bv a realistic energy distribution., Therefore this break may be washed out by a realistic energy distribution.1199" For the general case 0,=0. we calculate the afterglow helt curves nuuerically using equations (2). (9) and (10). the results are given in Fie.3 - Fig.6."," For the general case $\theta_v\neq 0$, we calculate the afterglow light curves numerically using equations (2), (9) and (10), the results are given in Fig.3 - Fig.6."1200 Frou these figures we see that the afterglow light curves are dependent on the values of ο. 0. and αν," From these figures we see that the afterglow light curves are dependent on the values of $\theta_v$, $\theta_c$ and $k$."

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